JP2006108533A - Position detection method and exposure method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position detection method and exposure method for highly precisely detecting the position information of a plurality of cell areas formed on an object, for carrying out superposition exposure to the respective cell regions by moving the object based on the detected position information, and for realizing highly precise exposure. <P>SOLUTION: In a step 411, the logarithm likelihood PL(M) with penalty of a model M following a parameter a<SB>jk</SB>calculated by performing an EGA arithmetic operation is calculated only from this time measurement result measured in a step 405. In a step 419, the value of logarithm likelihood PL(M') with penalty at the time of applying a weighted mean value a'<SB>jk</SB><SP>(s)</SP>of the parameter a<SB>jk</SB>corresponding to T<SB>jk</SB>larger than ζ to a formula (1) is calculated by referring to a matrix T. In a step 421, ζ is decremented by 1 until PL(M')<PL(M) is rejected or ζ=0, and in a step 425, a model M is displaced with a model M', and the processing is repeated, and the model where the value of the PL is finally satisfactory is selected as the optimal model. In a step 433, weight w when the weighted mean value is not selected is initialized to zero. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a position detection method and an exposure method. More specifically, the present invention relates to a position detection method for detecting position information of a plurality of partitioned areas respectively arranged on a plurality of objects, and a plurality of partitioned areas arranged on an object. The present invention relates to an exposure method in which a predetermined pattern is formed in each partitioned region by sequential exposure.

  In recent years, in a manufacturing process of a device such as a semiconductor element, an exposure apparatus such as a step-and-repeat system or a step-and-scan system, a wafer prober, or a laser repair apparatus is used. In these apparatuses, each of a plurality of shot areas arranged on a substrate is set to a predetermined reference point (for example, a rectangular coordinate system defined by a laser interferometer) that defines a moving position of the substrate (for example, Therefore, it is necessary to align (align) very precisely with respect to processing points of various apparatuses.

  In particular, in an exposure apparatus, a circuit pattern (reticle pattern) of 10 layers or more is superimposed and transferred onto a substrate (hereinafter referred to as “wafer”). The above characteristics can be inconvenient. In such a case, the chip does not satisfy the desired characteristics, and in the worst case, the chip becomes a defective product, which reduces the yield. Therefore, in the exposure apparatus, an alignment mark is previously attached to each of a plurality of shot areas on the wafer, and the position (coordinate value) of the mark in the stage coordinate system is detected. Thereafter, wafer alignment is performed for aligning one shot area on the wafer with the reticle pattern based on the mark position information and the position information of a known reticle pattern (which is measured in advance).

  As one of the wafer alignments, there is a global alignment method in which each shot area is aligned by detecting alignment marks of several shot areas on the wafer and obtaining regularity of the arrangement of the shot areas. Among them, an enhanced global alignment (EGA) method that accurately specifies the regularity of the arrangement of shot areas on a wafer by a statistical method has become the mainstream (see, for example, Patent Document 1 and Patent Document 2).

  In the EGA method, first, position coordinates on a stage coordinate system of a plurality of shot areas (hereinafter also referred to as “sample shot areas”) on a wafer are actually measured. The design positions of a plurality (three or more, usually about 7 to 15) of sample shot areas on the arrangement coordinate system defined by the actual measurement values and the shot area arrangement on the wafer. At the time of the conversion, statistical analysis processing (for example, least square method) is used so that the fitting error with the position coordinates obtained when the coordinates are converted to the position coordinates on the stage coordinate system is as small as possible. Error parameter values such as scaling, rotation, and offset used in the above are obtained. Further, the position coordinates of each shot region in the stage coordinate system are calculated based on the regression model defined by the obtained error parameter values.

  Various improvements have been made to the EGA method in order to meet the demand for higher overlay accuracy of shot areas accompanying the recent miniaturization of device patterns. For example, as a statistical model defined by the error parameter, a method using a regression model that considers in-shot components such as scaling and rotation in a shot area with respect to an array coordinate system as a parameter (see Patent Document 3), A method using a regression model that considers higher order components of the shot region array as a parameter (see Patent Document 4) is also used. In other words, in order to increase the overlay accuracy of shot areas, the regression model in the EGA method increases the degree of freedom of its parameters, and a more complicated regression model is adopted.

  However, in regression analysis such as the EGA method, if the degree of freedom of parameters is increased too much, overfitting (overlearning) occurs due to noise components, and so-called generalization error (overlearning (overfitting) does not occur. It is difficult to reduce a certain degree of error, for example, a modeling error when all shot regions are considered. For this reason, the proposal of the estimation method which can estimate a model with high robustness with respect to a noise component is desired.

JP-A 61-44429 JP-A-62-84516 JP-A-6-349705 Japanese Patent No. 3230271

According to a first aspect of the present invention, there is provided a position detection method for detecting position information of a plurality of partitioned areas (SA _p ) respectively arranged on a plurality of objects (W). When calculating the values of the plurality of parameters of the predetermined model that defines the arrangement of the plurality of partition regions, the information is obtained based on the detection result of the position information of at least some of the plurality of partition regions. In accordance with the value of a predetermined evaluation criterion to be obtained, the values of at least some of the plurality of parameters, the values of the parameter obtained only from the detection result, and the parameters obtained so far The position detection method is characterized in that the determination is made while changing the weight given to both based on both of the values.

  In this way, the model parameter value close to the true model parameter value representing the generalization error can be calculated based on the statistical evaluation criterion based on the actual position information of the partitioned area. Based on the model, the position information of the plurality of partitioned areas can be calculated with high accuracy.

From a second viewpoint, the present invention provides a position detection method for detecting position information of a plurality of partition regions (SA _p ) respectively arranged on a plurality of objects (W), and the plurality of partitions for each object. A value of a predetermined evaluation criterion obtained based on a detection result of position information of at least some of the plurality of partition regions when calculating the values of a plurality of parameters of the predetermined model that defines the region arrangement Depending on the parameter, the value of at least a part of the plurality of parameters is the value of the parameter obtained only from the detection result, or the parameter obtained so far including the value of the parameter It is a position detection method characterized by selecting whether it is set as the weighted average value of this value.

  According to this, when calculating the values of the plurality of parameters of the predetermined model that defines the arrangement of the plurality of partition areas formed on the object, the positional information of at least some of the plurality of partition areas Depending on the value of a predetermined evaluation criterion obtained based on the detection result of the above, the value of at least some of the plurality of parameters is set to the value of the parameter obtained only from the detection result, or the Select whether to use a weighted average value of the parameter values obtained so far, including the parameter value. In this way, the model parameter value close to the true model parameter value representing the generalization error can be calculated based on the statistical evaluation criterion based on the actual position information of the partitioned area. Based on the model, the position information of the plurality of partitioned areas can be calculated with high accuracy.

  According to a third aspect of the present invention, there is provided an exposure method for sequentially exposing a plurality of partition regions arranged on an object to form a predetermined pattern in each partition region, wherein the plurality of the plurality of partition regions are formed by the position detection method of the present invention. And a step of detecting the position information of the partitioned areas; and a step of exposing the partitioned areas by moving the object based on the detected position information. In such a case, the position information of a plurality of partition areas formed on the object by the position detection method of the present invention is detected with high accuracy, and the object is moved based on the detected position information. Since overlay exposure can be performed on the region, high-precision exposure can be realized.

  Hereinafter, an embodiment of the present invention will be described with reference to FIGS.

  FIG. 1 shows a schematic configuration of an exposure apparatus 100 according to an embodiment of the present invention. The exposure apparatus 100 is a step-and-scan projection exposure apparatus. The exposure apparatus 100 controls the illumination system 10, a reticle stage RST that holds a reticle R as a mask, a projection optical system PL, a wafer stage WST on which a wafer W as an object is mounted, an alignment detection system AS, and the entire apparatus. A main controller 20 and the like for controlling are provided.

  The illumination system 10 includes a light source, an illuminance uniformizing optical system including an optical integrator, a relay, as disclosed in, for example, Japanese Patent Application Laid-Open No. 2001-313250 (corresponding US Patent Application Publication No. 2003/0025890) It includes a lens, a variable ND filter, a variable field stop (also called a reticle blind or a masking blade), a dichroic mirror, and the like (all not shown).

In this illumination system 10, a slit-shaped illumination area (a rectangular illumination area elongated in the X-axis direction) defined by the reticle blind on the reticle R on which a circuit pattern or the like is drawn is substantially uniform by the illumination light IL. Illuminate with illuminance. Here, as the illumination light IL, far ultraviolet light such as KrF excimer laser light (wavelength 248 nm), vacuum ultraviolet light such as ArF excimer laser light (wavelength 193 nm), F ₂ laser light (wavelength 157 nm), or the like is used. . As the illumination light IL, it is also possible to use an ultraviolet bright line (g-line, i-line, etc.) from an ultra-high pressure mercury lamp.

  On reticle stage RST, reticle R is fixed, for example, by vacuum suction. Reticle stage RST is XY perpendicular to the optical axis of illumination system 10 (corresponding to optical axis AX of projection optical system PL described later) by a reticle stage drive unit (not shown) using a linear motor, a voice coil motor or the like as a drive source. It can be driven minutely in a plane and can be driven at a scanning speed specified in a predetermined scanning direction (here, the Y-axis direction which is the left-right direction in FIG. 1).

  The position of the reticle stage RST in the stage moving surface is always detected by a reticle laser interferometer (hereinafter abbreviated as “reticle interferometer”) 16 via a movable mirror 15 with a resolution of about 0.5 to 1 nm, for example. Is done. Here, actually, on the reticle stage RST, a moving mirror having a reflecting surface orthogonal to the Y-axis direction and a moving mirror having a reflecting surface orthogonal to the X-axis direction are provided, corresponding to these moving mirrors. A reticle Y interferometer and a reticle X interferometer are provided, but these are typically shown as a movable mirror 15 and a reticle interferometer 16 in FIG. Here, at least one of the reticle Y interferometer and the reticle X interferometer, for example, the reticle Y interferometer, is a two-axis interferometer having two measurement axes, and the reticle stage RST is based on the measurement value of the reticle Y interferometer. In addition to the Y position, the rotation amount (yawing amount) in the θz direction (rotation direction around the Z axis) can also be measured. Position information (including rotation information such as yawing amount) of reticle stage RST from reticle interferometer 16 is supplied to stage controller 19 and main controller 20 via this. The stage control device 19 drives and controls the reticle stage RST via a reticle stage drive unit (not shown) based on the position information of the reticle stage RST in response to an instruction from the main control device 20.

  Above the reticle R, a pair of reticle alignment detection systems 22 (however, in FIG. 1, the reticle alignment detection system 22 on the back side of the drawing is not shown) are arranged at a predetermined distance in the X-axis direction. Although not shown here, each reticle alignment detection system 22 includes an epi-illumination system for illuminating the detection target mark with illumination light having the same wavelength as the illumination light IL, and the detection target mark. And a detection system for capturing an image. The detection system includes an imaging optical system and an image sensor, and an imaging result (that is, a mark detection result by the reticle alignment detection system 22) by this detection system is supplied to the main controller 20. In this case, a deflection mirror (not shown) for guiding the detection light from the reticle R to the reticle alignment detection system 22 is movably arranged, and when an exposure sequence is started, based on a command from the main controller 20. The deflecting mirrors are retracted out of the optical path of the illumination light IL integrally with the reticle alignment detection system 22 by a driving device (not shown).

  The projection optical system PL is disposed below the reticle stage RST in FIG. 1, and the direction of the optical axis AX is the Z-axis direction. As the projection optical system PL, a birefringent optical system having a predetermined reduction magnification (for example, 1/5 or 1/4) is used.

  Wafer stage WST is arranged on a base (not shown) below projection optical system PL in FIG. Wafer holder 25 is placed on wafer stage WST. A wafer W is fixed on the wafer holder 25 by, for example, vacuum suction. Wafer stage WST is rotated by X, Y, Z, θz (rotation direction around Z axis), θx (rotation direction around X axis), and θy (rotation around Y axis) by wafer stage drive unit 24 in FIG. It is a single stage that can be driven in the direction of 6 degrees of freedom. For the remaining θz direction, wafer stage WST (specifically, wafer holder 25) may be configured to be rotatable, and yawing error of wafer stage WST is corrected by rotation on reticle stage RST side. It is also good.

  A movable mirror 17 that reflects a laser beam from a wafer laser interferometer (hereinafter abbreviated as “wafer interferometer”) 18 is fixed to a side surface of the wafer stage WST. The positions of the wafer stage WST in the X direction, the Y direction, and the θz direction (rotation direction about the Z axis) are always detected with a resolution of about 0.5 to 1 nm, for example.

  In the present embodiment, the X-axis and Y-axis interferometers are multi-axis interferometers having a plurality of measurement axes, and in addition to the X and Y positions of wafer stage WST, rotation (yawing (θz which is rotation around the Z axis) Rotation), pitching (θx rotation that is rotation around the X axis), and rolling (θy rotation that is rotation around the Y axis)) can also be measured.

  As described above, a plurality of wafer interferometers and moving mirrors are provided, but in FIG. 1, these are typically shown as moving mirror 17 and wafer interferometer 18.

  A reference mark plate FM is fixed in the vicinity of wafer W on wafer stage WST. The surface of the reference mark plate FM is set to the same height as the surface of the wafer W, and at least a pair of reticle alignment reference marks and a reference mark for baseline measurement of the alignment detection system AS are formed on this surface. Has been.

  The alignment detection system AS is an off-axis alignment sensor disposed on the side surface of the projection optical system PL. As this alignment detection system AS, for example, a broadband detection light beam that does not sensitize a resist on a wafer is irradiated onto a target mark, and an image of the target mark formed on a light receiving surface by reflected light from the target mark is not shown. An image processing type FIA (Field Image Alignment) type sensor that captures an image of an index using an imaging device (CCD) or the like and outputs an image pickup signal thereof is used. In addition to the FIA system, a target mark is irradiated with coherent detection light, and scattered light or diffracted light generated from the target mark is detected, or two diffracted lights (for example, of the same order) generated from the target mark. Of course, it is possible to use an alignment sensor for detecting the interference by using them alone or in combination as appropriate. The imaging result of the alignment detection system AS is output to the main controller 20 via an alignment signal processing system (not shown).

  In FIG. 1, the control system is mainly configured by a main control device 20 and a stage control device 19 subordinate thereto. The main controller 20 includes a so-called microcomputer (or workstation) including an internal memory such as a CPU (Central Processing Unit), a ROM (Read Only Memory), and a RAM (Random Access Memory). , To control the entire device.

  The main control device 20 includes, for example, an input device including a pointing device such as a keyboard and a mouse, a display device such as a CRT display (or liquid crystal display) (all not shown), and a CD (Compact Disc). , DVD (Digital Versatile Disc), MO (Magneto-Optical disc) or FD (Flexible Disc) information recording medium drive device 46 and a hard disk storage device 47 are connected externally. An information recording medium (hereinafter referred to as a CD) set in the drive device 46 has a program corresponding to a processing algorithm at the time of wafer alignment and exposure operations shown in the flowchart described later (hereinafter, “specific” for convenience). Other programs, and databases attached to these programs are recorded.

  The main controller 20 executes processing according to the above-described specific program so that, for example, the exposure operation is performed accurately, and performs, for example, synchronous scanning of the reticle R and the wafer W, stepping of the wafer W, etc. Control is performed based on the measurement value of the wafer interferometer 18.

  Further, the exposure apparatus 100 of the present embodiment supplies an image forming light beam for forming a plurality of slit images toward the best image forming surface of the projection optical system PL from an oblique direction with respect to the optical axis AX direction (not shown). And an oblique incidence type multi-point focus detection system comprising a light receiving system (not shown) that receives each reflected light beam of the imaging light beam on the surface of the wafer W through a slit. As this multipoint focus detection system, one having the same configuration as that disclosed in, for example, Japanese Patent Laid-Open No. 6-283403 is used, and the output of this multipoint focus detection system is supplied to the main controller 20. Yes. Main controller 20 drives wafer stage WST in the Z direction and the tilt direction via stage controller 19 and wafer stage drive unit 24 based on the wafer position information from the multipoint focus detection system.

  Next, with respect to the operation when performing exposure processing of the second layer (second layer) and subsequent layers on the wafer W by the exposure apparatus 100 of the present embodiment configured as described above, the wafer of FIG. 3 and FIG. 4 showing the processing algorithm of the CPU in the main control device 20 executed according to the specific program will be described.

  As a premise, it is assumed that the specific program and other programs in the CD-ROM set in the drive device 46 are installed in the storage device 47. Furthermore, it is assumed that the reticle alignment and baseline measurement processing programs are loaded from the storage device 47 to the internal memory of the main control device 20 by the CPU in the main control device 20.

On the wafer W, as shown in FIG. 2, a plurality of (for example, N) shot areas SA _p are formed in a matrix arrangement in the processing steps up to the previous layer, and between adjacent shot areas. A wafer alignment X mark (wafer X mark) MX _p and a wafer alignment Y mark (wafer Y mark) MY _p are formed on a street line having a width of about 100 μm. Among, X position of wafer X mark MX _p is consistent in design to the X-coordinate of the shot area SA _p (center C _p of), Y position of wafer Y mark MY _p is shot area SA _p (the center C _It is designed to match the Y coordinate of _p ). That is, in design, the position coordinates of the shot area SA _p (center C _p ) are obtained from the X position of the wafer X mark MX _p and the Y position of the wafer Y mark MY _p .

  Information relating to the shot area on the wafer W as described above (so-called shot map data relating to the number of shots, shot size, arrangement, alignment mark arrangement, type, etc.) is downloaded to the storage device 47 from the host computer of the lithography system. It is assumed that

  As shown in FIG. 3, first, in step 301, reticle R is loaded onto reticle stage RST via a reticle loader (not shown). When this reticle loading is completed, from step 303 to step 305, main controller 20 (more precisely, CPU) performs reticle alignment and baseline measurement according to the above-described reticle alignment and baseline measurement processing program as follows. And run.

  That is, main controller 20 positions reference mark plate FM on wafer stage WST via wafer stage drive unit 24 at a predetermined position directly below projection optical system PL (hereinafter referred to as “reference position” for convenience). A relative position between the pair of first reference marks on the reference mark plate FM and the pair of reticle alignment marks on the reticle R corresponding thereto is detected using the pair of reticle alignment detection systems 22 described above. Then, main controller 20 stores the detection result of reticle alignment detection system 22 and the measurement values of interferometers 16 and 18 at the time of detection in a memory. Next, main controller 20 moves wafer stage WST and reticle stage RST in the opposite directions along the Y-axis direction by a predetermined distance, respectively, to generate another pair of first reference marks on reference mark plate FM. And a corresponding pair of reticle alignment marks on the corresponding reticle R are detected using the above-described pair of reticle alignment detection systems 22. Then, main controller 20 stores the detection result of reticle alignment detection system 22 and the measurement values of interferometers 16 and 18 at the time of detection in a memory. Next, in the same manner as described above, the relative positional relationship between another pair of first reference marks on the reference mark plate FM and the corresponding reticle alignment mark may be further measured.

  Then, main controller 20 obtains information on the relative positional relationship between the at least two pairs of first reference marks obtained in this way and the corresponding reticle alignment marks, and the measurements of interferometers 16 and 18 during the respective measurements. Value is used to define a reticle stage coordinate system defined by the measurement axis of the interferometer 16 and a wafer stage coordinate system defined by the measurement axis of the interferometer 18 (hereinafter abbreviated as “stage coordinate system”). Is obtained. Thereby, reticle alignment is completed.

  Next, in step 305, baseline measurement is performed. Specifically, wafer stage WST is returned to the above-mentioned reference position, moved from the reference position by a predetermined amount, for example, the design value of the baseline, in the XY plane, and then moved onto reference mark plate FM using alignment detection system AS. The second reference mark is detected. In main controller 20, the information on the relative positional relationship between the detection center of alignment detection system AS and the second reference mark obtained at this time and the pair of first measurements measured when wafer stage WST is first positioned at the reference position. Based on the information on the relative positional relationship between the pair of reticle alignment marks corresponding to the reference mark and the measurement value of the wafer interferometer 18 at each measurement, the baseline of the alignment detection system AS, that is, the projection center of the reticle pattern, The distance (positional relationship) from the detection center (index center) of the alignment detection system AS is calculated.

When such a series of preparation operations is completed, the main controller 20 unloads the above-described reticle alignment and baseline measurement processing programs from the memory, and loads the above-described specific program from the storage device 47 into the memory. Thereafter, in accordance with the particular program, the wafer loading and overlay exposure for each shot area SA _P on the wafer W wafer alignment (wafer alignment by the EGA method in this case) is performed.

  First, in step 307, the wafer number s is initialized to “1”, and a weight w described later is initialized to “0”. In the next step 309, the wafer W is loaded onto the wafer holder 25 on the wafer stage WST via a wafer loader (not shown). Here, in this embodiment, prior to loading of the wafer W, a pre-alignment apparatus (not shown) defines a stage coordinate system (XY coordinate system) that defines the movement position of the wafer stage WST, and a shot area on the wafer W. The rotational deviation and center position deviation of wafer W with respect to wafer stage WST are such that the coordinate system defined by the arrangement (αβ coordinate system in FIG. 2, hereinafter abbreviated as “wafer coordinate system”) matches to some extent. It is assumed that so-called pre-alignment that is adjusted with high accuracy is performed, and so-called search alignment that adjusts the rotational deviation and center position deviation of the wafer W after loading is unnecessary.

  Next, in subroutine 311, wafer alignment processing is performed. In this wafer alignment process, the arrangement of shot areas on the wafer W in the stage coordinate system is estimated, and the arrangement, that is, the center position of all shot areas is calculated. The wafer alignment process will be described later in detail.

  Next, in step 313, 1 is set to the value of the counter p indicating the array number of the shot area (hereinafter referred to as “counter value p”), and the first shot area is set as the exposure target area.

  Next, in step 315, based on the alignment coordinates of the exposure target area calculated in the subroutine 311 (center position coordinates of each shot area), acceleration for the position of the wafer W to expose the exposure target area on the wafer W is performed. Wafer stage WST is moved via stage control device 19 and wafer stage drive unit 24 so as to be the start position, and stage control device 19 and reticle stage drive unit (such that the position of reticle R is the acceleration start position). The reticle stage RST is moved through (not shown).

  In step 317, relative scanning of reticle stage RST and wafer stage WST is started. When both stages reach their respective target scanning speeds and reach a constant speed synchronization state, the pattern area of the reticle R starts to be illuminated by the illumination light IL from the illumination system 10, and scanning exposure is started. Then, different areas of the pattern area of the reticle R are sequentially illuminated with the illumination light IL, and the scanning exposure is completed when the illumination on the entire pattern area is completed. Thereby, the pattern of the reticle R is reduced and transferred to the exposure target area on the wafer W via the projection optical system PL.

  In step 319, with reference to the counter value p, it is determined whether exposure has been performed for all shot areas. Here, since p = 1, that is, only the first shot area has been exposed, the determination at step 319 is denied and the routine proceeds to step 321.

  In step 321, the counter value p is incremented (p ← p + 1), the next shot area is set as the exposure target area, and the process returns to step 315.

  Thereafter, the processing and determination of step 315 → step 317 → step 319 → step 321 are repeated until the determination in step 319 is affirmed. When the transfer of the pattern to all shot areas on the wafer W is completed, the determination in step 319 is affirmed, and the process proceeds to step 323.

  In step 323, an instruction to unload the wafer W is given to a wafer loader (not shown). As a result, the wafer W is unloaded from the wafer holder 25 and then transferred to a coater / developer (not shown) connected inline to the exposure apparatus 100 by a wafer transfer system (not shown).

  In the next step 325, it is determined whether or not the exposure of all wafers in the lot has been completed. If this determination is affirmative, the exposure process is terminated, and if negative, the process returns to step 309. Here, since the exposure of the first (first) wafer W in the lot has only been completed, the determination is denied and the process returns to step 309.

  Thereafter, step 309 (wafer load) → subroutine 311 (wafer alignment) → step 313 to step 321 (exposure) → step 323 (wafer unload) → step 325 (lot) until the determination in step 325 of FIG. 3 is affirmed. (End judgment) loop processing is sequentially executed for each wafer in the lot. If the determination in step 325 is affirmative, the series of exposure processing is terminated.

  That is, in the above exposure processing, wafer alignment processing and exposure processing are performed on wafers in a lot, with wafers sequentially loaded on wafer stage WST being processed.

≪Wafer alignment process≫
Next, the wafer alignment process in the subroutine 311 will be described. In this wafer alignment process, the EGA method is employed. Here, the EGA method will be described first.

Wafer marks MX _p formed on the wafer W shown in FIG. 2, the actual forming position of the MY _p is deviated from the design position of (i.e. formation position of the shot area SA _P is shifted from the designed position), a wafer stage WST This is because of a mismatch between the stage coordinate system (X, Y) that defines the movement position of the wafer and the wafer coordinate system (α, β).

Deviation between the design position coordinate x (= (x ₁ , x ₂ )) of the center position C _p of the shot area SA _p and the actual position coordinate (x ₁ ′, x ₂ ′) caused by this mismatch. Is y (= (x ₁ ′ −x ₁ , x ₂ ′ −x ₂ )). A model expression indicating the relationship between the design position coordinates x and y is expressed by the following expression. In the following, it is assumed that the position coordinates corresponding to the X axis of the stage coordinate system are x ₁ and x ₁ ′, and the position coordinates corresponding to _the Y axis are x ₂ and x ₂ ′.

ここで、ａ^tは、Ｍ×２の行列ａの転置行列であり、この行列ａの各要素ａ_jkがこのモデル式のパラメータとなる。また、ψ（ｘ）は、次式で示されるＭ次元のｘ（＝（ｘ₁，ｘ₂））の多項式であり、εは、正規分布に従うランダム変数（ランダム誤差）を各要素とする２次元ベクトルである。

Here, a ^t is a transposed matrix of the matrix a of M × 2, each element a _jk of the matrix a is a parameter of the model equation. Also, ψ (x) is an M-dimensional x (= (x ₁ , x ₂ )) polynomial expressed by the following equation, and ε is a random variable (random error) that follows a normal distribution as 2 elements. It is a dimension vector.

ただし、このパラメータａ_jkは、互いに規格直交化されたパラメータであるものとする。通常のＥＧＡでは、それぞれが、ステージ座標系に対するウエハ上のショット領域の配列によって規定されるウエハ座標系の回転、倍率、オフセットをそのまま表すパラメータを用いていたが、この状態では、各パラメータが相関性を持ち、後述するように、重み付け平均をそのパラメータの値として用いたり、別の演算により算出された値を他のパラメータの値として用いたりすることが困難となる。そこで、本実施形態では、通常のＥＧＡパラメータを規格直交化し、直交化後のパラメータａ_jkを用いて、ＥＧＡ演算を行うこととする。ここで、ＥＧＡパラメータの規格直交化には、例えば公知のグラム−シュミット（Ｇｒａｍ−ｓｃｈｍｉｄｔ）の方法を用いることができるので、詳細な説明を省略する。このようにパラメータの規格直交化を行い、パラメータの重み付け平均演算によりパラメータの値を算出する処理は、最小二乗法によりパラメータの最尤推定値を求めることとほぼ等価である。

However, this parameter a _jk is assumed to be a parameter orthogonalized to each other. In normal EGA, parameters that directly represent the rotation, magnification, and offset of the wafer coordinate system defined by the arrangement of shot areas on the wafer with respect to the stage coordinate system are used. In this state, each parameter is correlated. As will be described later, it is difficult to use the weighted average as the value of the parameter or to use the value calculated by another calculation as the value of the other parameter. Therefore, in the present embodiment, normal EGA parameters are standardized orthogonally, and EGA computation is performed using the orthogonalized parameters a _jk . Here, since the known Gram-schmidt method can be used for the standard orthogonalization of the EGA parameters, for example, detailed description is omitted. The process of performing the parameter orthogonalization in this way and calculating the parameter value by the weighted average calculation of the parameter is almost equivalent to obtaining the maximum likelihood estimation value of the parameter by the least square method.

すなわち、ψ（ｘ）は、設計上の位置座標（ｘ₁，ｘ₂）に関する多項式を各要素とする１次元ベクトルである。上記式（１）によれば、設計上の位置座標（ｘ₁，ｘ₂）と、実際の位置座標（ｘ₁’，ｘ₂’）とのずれｙは、設計上の位置座標（ｘ₁，ｘ₂）の多項式の線形結合により表現することができる。

That, [psi (x) is a polynomial related to the position coordinates of the design (x _1, x ₂₎ is a one-dimensional vector whose elements. According to the above formula (1), the deviation y between the design position coordinate (x ₁ , x ₂ ) and the actual position coordinate (x ₁ ′, x ₂ ′) is the design position coordinate (x ₁ , X ₂ ) can be expressed by a linear combination of polynomials.

  In this embodiment, since the parameter of the model formula is calculated for each wafer in the wafer alignment process of the subroutine 311, the wafer number s is given to the model formula of the above formula (1), and the following formula: It shall be expressed as

すなわち、この式は、ウエハ番号ｓのウエハＷでのモデル式となる。なお、ここで、ｉは、計測されるマークの番号（マーク番号）を表す。

That is, this equation is a model equation for wafer W with wafer number s. Here, i represents the number of the mark to be measured (mark number).

The EGA system, the position of the design of the shot area SA _g, are substituted into the model equation of the equation (4) determines the actual position of the shot area SA _g, its location, the shot area in the stage coordinate system SA _For this purpose, it is necessary to obtain the value of the parameter a _jk ^(s) that is each element of the matrix a ^(s) in the model formula of the above formula (4). Therefore, in this embodiment, several (for example, h) wafer marks attached to some shot areas SA _i (i = 1, 2,..., N) out of the shot areas SA _i of the wafer W. The position (MX ′ _g , MY ′ _g ) in the stage coordinate system is measured, and the design position of the sample shot SA _{g and} the design position (MX in the in-shot coordinate system of the h measured wafer marks) are measured. _g , MY _g ) and statistical processing (for example, least square method) based on the model expression shown in the above equation (4), and the value of the evaluation function E shown in the following equation is The value of the parameter a _jk ^(s) in the model equation of the above equation (4) is estimated.

すなわち、この評価関数Ｅは、計測される各ウエハマークＭ_i,Kの位置の予想位置（ＭＸ_g’，ＭＹ_g’）とその位置の実測値（ＭＸ_g，ＭＹ_g）との残差の二乗和を、ウエハマークのサンプル数ｈで割ったもの（すなわち残差の二乗和の平均）である。

In other words, this evaluation function E is the residual of the expected position (MX _g ′, MY _g ′) of the position of each wafer mark M _{i, K} to be measured and the actual measurement value (MX _g , MY _g ) of that position. This is the sum of squares divided by the number h of wafer mark samples (that is, the average of the residual sum of squares).

In the present embodiment, for the parameter a _jk ^(s) of the model formula shown in the above formula (4), for example, from the empirically obtained property (attribute) of each parameter, It is classified in advance according to the magnitude of the fluctuations.

A matrix serving as an index for classification of the parameters is a matrix T. This matrix T is a 2 × M matrix, and each element is T _jk . The element T _jk corresponds to each element a _jk of the parameter matrix a, and takes one of 0, 1, and 2. The parameter a _jk is classified according to the value of T _jk . For example, regarding the transition level T _jk corresponding to the parameter a _jk that seems to have a large value variation between wafers, the value is set to 0, or the value variation between wafers is not so large. For T _jk corresponding to the parameter a _jk that seems to have a large variation in value, the value is set to 1, or the value of T _jk that seems to have a smaller variation is set to 2 . For example, the matrix shown below can be set as the matrix T.

この例においては、（ｘ₁，ｘ₂）の１次成分に対応するパラメータａ_jkに対応するＴ_jkの値が０に設定されており、（ｘ₁，ｘ₂）の２次成分に対応するパラメータａ_jkに対応するＴ_jkの値が１に設定されており、（ｘ₁，ｘ₂）の３次以上の成分に対応するパラメータａ_jkに対応するＴ_jkの値が２に設定されている。なお、Ｔ_jkは、上記式（６）に示される設定例に限定されるものではなく、様々な値を設定することができる。しかし、ここでは、上記式（６）の設定がなされたものとして話を進める。

In this example, corresponds to the second-order component of (x _1, x ₂₎ the value of T _jk corresponding to the parameter a _jk corresponding to the primary component of the is set to 0, (x _1, x ₂₎ the value of T _jk corresponding to the parameter a _jk for is set to 1, is set to (x _1, x ₂₎ the value of T _jk corresponding to the parameter a _jk corresponding to the third order or more components of 2 ing. Note that T _jk is not limited to the setting example shown in the above formula (6), and various values can be set. However, the description will proceed here assuming that the above equation (6) has been set.

  It should be noted that such parameter classification has already been performed by an operator via an input device (not shown), and the designated content is stored in the storage device 47.

  Hereinafter, the wafer alignment processing will be described along the flowchart of the subroutine 311 shown in FIG. As described above, this subroutine 311 is executed once for the wafer every time the wafer to be processed is switched. Therefore, in the following description, the processing flow when the wafer at the head of the lot is the processing target will be described first, and then the processing flow when the second, third,. Will be explained in turn. As described above, when processing the first wafer of the lot, the wafer number is initialized to “1” in step 307 of FIG. 3, and the weight w of each parameter is set to “0”. It is assumed that

In step 401, the sample information of the wafer W is referred. In the EGA processing, as described above, several shot areas are selected as sample shots SA _g from the shot areas SA _i on the wafer W, and the wafer marks attached to the sample shot areas SA _g are selected. , The positions (MX _g , MY _g ) (g = 1, 2,..., H) of a total of h sample shot areas are measured. The sample information is information regarding the number and arrangement of sample shot areas to be measured. Here, it is assumed that the number and arrangement of wafer marks M _{i, k in} the sample shot area satisfying such an effective number of samples are stored in the storage device 47, the sample information is acquired from the storage device 47, and the internal It is assumed that the information is stored in a memory and referred to. It is assumed that a sufficient number of samples and arrangement are specified as the sample information.

In the next step 403, the sample h pieces of wafer marks arranged in the shot area SA _i which is designated as the sample shot area on the information, based on the measurement order specified in the sample information, alignment detection system AS The wafer stage WST is moved in the XY plane so as to move sequentially within the detection field of view, and the wafer mark WST is imaged by the alignment detection system AS, and the position of the wafer stage WST at that time is determined by the wafer interferometer 18. Obtain from the measured value. Since the alignment detection system AS sends the position information of the wafer marks Mi _{, K} within the imaging field of view, the stage coordinates are determined from the position information of the wafer marks, the measurement values of the wafer interferometer 18 and the baseline. An actual measurement value of the position of the wafer mark in the system can be obtained. The actually measured value of the obtained wafer mark is held in the memory. In this way, the actual measurement values (MX _g , MY _g ) of the positions of the h wafer marks attached to the sample shot SA _i specified in the sample information are acquired.

In the next step 405, the value of the parameter of the model formula (4) is calculated when only the current measurement result is used. A parameter a _jk that minimizes the evaluation function E shown in the above equation (5) based on only the actually measured values (MX _g , MY _g ) of the position of each wafer mark stored in the internal memory, that is, satisfies the following equation: The value a _jk ^′ is obtained using the least square method.

  In the next step 407, it is determined whether or not the weight w is “0”. If the determination is affirmed, the process proceeds to step 431. If the determination is negative, the process proceeds to step 409. When processing the first wafer at the head of the lot, since the weight w remains set to “0” in step 307 of FIG. 3, the determination is affirmed and the process proceeds to step 431.

In step 431, the model M, that is, the model based on the parameter a _jk ′ based only on the current measurement result is selected as the optimum model. In the next step 433, the weight w is adjusted. Here, for a parameter for which the weighted average value is selected as the optimal value, the weight w is incremented by “1”, and for a parameter for which the weighted average value is not selected as the optimal value, the weight w Is initialized to “1”. Here, since the weighted average value is not selected for all parameters, the weight w for all parameters is initialized to “1”. In the next step 435, the finally calculated value a _jk ′ of each parameter is stored as it is as the optimum value a _jk ^(s) , and in step 437, the center position coordinates of all the shot areas SA _p are calculated. In step 439, the wafer number s is incremented by one. After step 439, the subroutine 311 is terminated.

  As described above, when the first wafer of the lot is the object to be processed and the optimum values of the past parameters have not been calculated yet, the weighted average cannot be calculated. The parameter value obtained only from the actual measurement value is selected as the optimum value as it is (that is, the model M is selected).

Next, a processing flow when the second wafer is a processing target will be described. Here, the wafer number s is “2” and the weight w is “1” by the processing of the subroutine 311 for the first wafer. After step 401 (sample information acquisition), step 403 (sample shot measurement), and step 405 (calculation of parameter a _jk value a _jk ′ based only on the current measurement result) are executed in the same manner as the first wafer. Step 407 is executed.

In step 407, when processing the first wafer W, the weight w is set to “1”, and the determination is negative. In step 409, the obtained parameter value a _jk ^′ is set in the above equation (4), and the design position of the center C _g of the sample shot area SA _g is substituted into the above equation (4) for prediction. Determine the position of the sample shot to be played. Then, a residual between the obtained position of the sample shot area and the actually measured value of the sample shot area is obtained.

In the next step 411, a log-likelihood PL (M) with a penalty is calculated for a model (this is model M) in which the value of the parameter a _jk is a value a _jk ′ obtained based only on the current measurement result. To do. PL (M) is expressed by the following equation.

このペナルティ付き対数尤度ＰＬ（Ｍ）においては、値が大きい方が、最も尤もらしいモデルであると評価される。ＰＬ（Ｍ）における第２項のβ（ｎ）・ｄ（ζ）は、ペナルティ項である。このβ（ｎ）を「２」とおけば、ＰＬ（Ｍ）は、赤池情報量規準（ＡＩＣ：Akaike's Information Criterion）に相当する尤度となり、β（ｎ）を「ｌｏｇｎ」とおけば、ＰＬ（Ｍ）は、ベイジアン情報量規準（ＢＩＣ：Bayesian Information Criterion）に相当する尤度となる。β（ｎ）の値は、シミュレーション等によって決定することができるが、サンプル数（すなわちｎ）に依存した関数とすることができる。なお、このβ（ｎ）の設定方法などについては後述する。

In the log-likelihood likelihood PL (M) with a penalty, the larger value is evaluated as the most likely model. The second term β (n) · d (ζ) in PL (M) is a penalty term. If β (n) is set to “2”, PL (M) becomes a likelihood corresponding to the Akaike's Information Criterion (AIC), and if β (n) is set to “logn”, PL (M) is a likelihood corresponding to a Bayesian Information Criterion (BIC). The value of β (n) can be determined by simulation or the like, but can be a function depending on the number of samples (that is, n). A method for setting β (n) will be described later.

  As an example of such likelihood L, for example, an expected value of the amount of change in residual with respect to an increase in parameters can be employed. d (ζ) is the number of unknown parameters. As described above, the number of unknown parameters is a number depending on ζ.

In the next step 413, the value of the counter ζ (hereinafter referred to as “counter value ζ”) is initialized. This counter value ζ is a counter value used for comparison with each element T _jk of the matrix T, and its possible value corresponds to a possible value of T _jk . That is, in the above example, since T _jk = 0, 1, and 2, ζ also takes either 0, 1, or 2. Therefore, in this case, the maximum value ζ _max of ζ is “2”, and the counter value ζ is initialized to “2” here.

In the next step 415, the matrix T is referred to, and the value of the parameter a _jk ^(s) corresponding to T _jk smaller than the counter value ζ is set to a _jk ′ calculated in step 405, and T _jk equal to or larger than the counter value ζ is set. The other parameters a _jk ^(s) corresponding to are calculated using a weighted average calculation represented by the following equation.

ここで、ａ_jk’は、上記ステップ４０５で算出されたパラメータａ_jkの値であり、ａ_jk ^(s-1)は、前回のウエハＷでの処理のステップ４３７において記憶装置４７に記憶されたパラメータの値である。すなわち、ａ_jk ^(s)は、過去に算出されたパラメータａ_jkの値ａ_jk ^(s-1)と、今回算出されたパラメータａ_jkの値ａ_jk’の重み付け平均値となる。なお、Ｔ_jk≧ζに対応する上記パラメータａ_jkの値が重み付け平均値となり、Ｔ_jk＜ζに対応するパラメータａ_jkの値がａ_jk ^'となるモデルをモデルＭ’とする。

Here, a _jk ′ is the value of the parameter a _jk calculated in step 405 above, and a _jk ^(s−1) is stored in the storage device 47 in step 437 of the previous processing on the wafer W. The value of the parameter. That is, a _jk ^(s) is a weighted average value of the value a _jk ^{(s−1) of} the parameter a _jk calculated in the past and the value a _jk ′ of the parameter a _jk calculated this time. A model in which the value of the parameter a _jk corresponding to T _jk ≧ ζ is a weighted average value and the value of the parameter a _jk corresponding to T _jk <ζ is a _jk ^′ is a model M ′.

In the next step 417, a residual when the parameter a _jk ^(s) calculated in the above step 415 is applied to the equation (4) is calculated. In step 419, a logarithmic likelihood with a penalty in the model M ′ is calculated. The value of PL (M ′) is calculated.

  In the next step 421, PL (M) and PL (M ') are compared to determine whether PL (M') <PL (M). If this determination is affirmed, the process proceeds to step 423, and if not, the process proceeds to step 431. Here, the discussion proceeds assuming that the judgment is affirmed.

  In the next step 423, ζ is decremented by 1, and in step 425, the model M is replaced with the model M ′. In step 427, it is determined whether or not the counter value ζ is “0”. If this determination is affirmed, the process proceeds to step 429, and if not, the process returns to step 415. Here, since ζ is “1”, the determination is negative and the routine returns to step 415.

In step 415, the transition matrix T is referred to, the weighted average value of the parameter a _jk corresponding to T _jk greater than or equal to the counter value ζ is calculated using the above equation (9), and the residual is calculated in step 417. In step 419, PL (M ′) is calculated, and in step 421, it is determined whether PL (M ′) <PL (M). If this determination is negative, the process proceeds to step 431, and if the determination is positive, the process proceeds to step 423.

  If the determination is affirmative and the routine proceeds to step 423, ζ is again decremented by “1”, the model M ′ is replaced with the model M at step 425, and whether or not the counter value ζ is “0” at step 427. Is judged. Here, since the counter value ζ is “0”, the determination is affirmed and the routine proceeds to step 429. In step 429, the model M ′ having the best PL value so far is selected as the optimum model. On the other hand, if the determination in step 421 is negative and then the process proceeds to step 431, the model M is selected as the optimum model.

In step 433 performed after performing step 429 or step 431, the weight w is incremented by “1” for the parameter for which the weighted average value is selected, and the weight w is set for the parameter for which the weighted average value is not selected. It is initialized to “1”. In the next step 435, the value of each parameter selected as the optimum model is stored as a _jk ^(s) . In step 437, the reference positions of all shot areas are calculated and stored. In step 439, the wafer number s is calculated. Is incremented by one. After completion of step 439, the subroutine 311 is terminated.

As described above, the second wafer W has the best penalty likelihood logarithm while increasing the parameter whose value is the weighted average so far according to the transition level T _jk registered in the transition matrix T. Select the optimal model. A process similar to the process for the second wafer W is also performed on the third and subsequent wafers W.

  In this embodiment, in step 307 of FIG. 3, the weight w is set to 0, and the optimization of the model is not performed by the parameter weighted average calculation for the first wafer at the head of the lot. The model may be optimized by weighted average calculation of parameters across lots. At this time, in step 307 of FIG. 3, the weight w may be initialized to “1”. In this way, the determination at step 407 is denied from the time of processing the first wafer, the processing after step 409 is performed, and it is determined whether or not the weighted average value is selected as the parameter value. The process can be executed.

  As is clear from the above description, according to the present embodiment, the subroutine 311 corresponds to a process of detecting position information of a plurality of shot areas using the position detection method according to the present embodiment. Step 321 corresponds to a step of performing overlay exposure on each shot area by moving wafer stage WST (wafer W) based on position information measured using alignment detection system AS.

As described above in detail, according to the present embodiment, the value a of the plurality of parameters a _jk of the predetermined model (the above formula (4)) that defines the arrangement of the plurality of shot regions formed on the wafer W. _In calculating _jk ^(s) , in the subroutine 311, a penalty-like log likelihood PL (M) obtained based on the detection result of the position information of at least some of the shot areas SA _p among the plurality of shot areas SA _p. The value of at least a part of the parameters a _jk of the plurality of parameters a _jk in accordance with the values of the parameters obtained from only the measurement result of the position information of the sample shot area on the wafer W at this time Or the weighted average value of the past values of the parameter a _jk obtained so far including the value of the parameter is selected. In this way, a model close to the value of the true model parameter representing the generalization error based on the logarithmic likelihood PL (M) with a penalty, which is a statistical evaluation criterion based on the position information of the actual shot region. Since the values of the parameters can be calculated, the position information of the plurality of shot areas can be calculated with high accuracy based on the model.

In the present embodiment, the values of at least some of the parameters a _jk are obtained for the parameters obtained from only the measurement result of the position information of the sample shot area on the wafer W this time and the previous wafers. The parameter a _jk may be obtained by performing a weighted average calculation while continuously changing the weight (contribution) given to the past value of the parameter a _jk .

Further, according to the present embodiment, when the value of the parameter a _jk obtained only from the actual measurement value of the position information of the sample shot area of the wafer to be processed is selected in step 433, The weight w of the value of the parameter a _jk obtained previously is set to “0”. In this way, it is possible to quickly calculate the weighted average of the parameters for the next and subsequent wafers using the weight w.

In addition, according to the present embodiment, the plurality of parameters a _jk that define the model formula are parameters orthogonalized to each other, and thus can be obtained by weighted average calculation without considering the correlation between the parameters. Since the model can be configured with the value of the parameter and the value of another parameter obtained by another method, the parameter can be easily identified.

  In the present embodiment, the position coordinates of each shot area are calculated using the model formula defined by the parameters that have already been standardized orthogonally, but the parameters that have been standardized orthogonally are converted into normal EGA parameters. Alternatively, the position coordinates on the stage coordinate system of each shot area may be obtained.

  Further, according to the present embodiment, the weighted average value of the parameter values obtained in the past and the parameter value obtained only from the actual measurement value of the position information of the sample shot area on the wafer W to be processed. Based on the value, the weighted average value of the parameter value obtained so far, including the value of the parameter, is obtained by the sequential calculation shown in the equation (9). In this way, it is not necessary to store past parameter values one by one when performing parameter weighting calculations, and the calculation time can be shortened.

  In addition, according to the present embodiment, when performing the sequential calculation shown in the above equation (9), the weight given to the weighted average value of the parameter value obtained in the past contributes to the calculation of the weighted average value. The number of wafers W that have been processed. The number of wafers W is naturally an appropriate weight for the value calculated this time as a weight for the past parameter.

However, the calculation formula for this parameter can be further adjusted. For example, the forgetting coefficient e ^−P for reducing the weight of the weighted average value of the parameter value obtained in the past is used as the weight with the number w of wafers W contributing to the calculation of the weighted average value. You may make it use the weighted average arithmetic expression of the parameter shown by following Formula multiplied by sequential calculation.

この忘却係数とは、パラメータの値に対する重みを過去になればなるほど減じていき、過去のパラメータの値の重みを徐々に軽減していくための係数である。したがって、この忘却係数を用いれば、上記式（９）に対して、過去のパラメータの重みを軽くして、最近のパラメータの値の重みを重くすることができるようになる。

The forgetting factor is a factor for gradually reducing the weight of the past parameter value by decreasing the weight for the parameter value as the past. Therefore, if this forgetting factor is used, the weight of the past parameter can be reduced and the weight of the recent parameter can be increased with respect to the equation (9).

  As described above, various parameter weights can be used, but basically, a value corresponding to the reliability of the parameter value is obtained as the weight when the parameter value is obtained. do it.

  In the above-described embodiment, which of the model M and the model M ′ is selected is determined based on the criterion (logged likelihood with a penalty). Judgment based on this criterion can be said to be based on statistical validity, but the most important point in wafer alignment is to make the alignment accuracy as good as possible, that is, to make the residual as small as possible. . Therefore, for example, even when an optimum model is selected, a threshold value is set for the residual value in the model M ′, and if the residual is larger than that value, the wafer mark of the sample shot is further set. The additional measurement may be performed, and then the model M and the model M ′ may be compared again.

<Evaluation results>
Note that, as in this embodiment, estimation using the estimated value of the parameter as the weighted average of the measured value of the position information of the sample shot area obtained this time and the value of the parameter obtained in the past assumes a prior distribution. MAP (Maximum A Posterior) estimation (maximum posterior probability estimation). In the following, when estimating the parameter values of the model in the present embodiment, the simulations shown below for comparison between when the MAP estimation method is used and when using another estimation method, and the specific method for setting the penalty It demonstrates using a result.

  In the model employed in this simulation, for example, the parameter group of the first order term in the above equation (4) is set as the first group, and the parameter group of the second and third order terms in the above equation (4) is set as the second group. The first group transition is assumed to occur for each wafer, and the first group transition probability q1 is set to 1, and the first group transition fluctuation degree (standard deviation) σ1 is set to 0. Also, it is assumed that the transition of the second group occurs probabilistically (assuming that the error model follows a normal distribution), and the transition probability q2 of the second group is a value from 0.001 to 0.1. The simulation was performed by setting a value from 0.001 to 0.01 as the transition magnitude (standard deviation) σ2 of the second group.

  In this simulation, the number of trials was 100, and each trial was performed based on data of 200 consecutive wafers. In addition, it is assumed that a shot area of all 61 shots is formed on each wafer. Furthermore, the number of samples was set to 20 shots, except for the simulation results shown in FIGS. Further, except for the simulation results shown in FIGS. 7A and 7B, the transition probability of the second group was set to 0.01. Further, except for the simulation results shown in FIGS. 8A, 8B, and 8C, the transition magnitude (standard deviation) σ2 of the second group was set to 0.002.

This MAP estimation method can be compared with a so-called ML (Maximum Likelifood) estimation method. This ML estimation method is different from the MAP estimation method in that a parameter value obtained in the past is used as it is for a parameter _satisfying ζ ≦ T _jk instead of a weighted average of parameters.

  FIG. 5 (A) shows an evaluation result by simulation of overlay error when EGA is performed using the ML estimation method, and FIG. 5 (B) shows EGA using the MAP estimation method. The evaluation result by the simulation of the overlay error when it is performed is shown. Here, in both figures, the horizontal axis is the value of penalty β (n), and the vertical axis is the root mean square value of the generalization error. 6A to 8C, the horizontal axis is the value of penalty β (n), and the vertical axis is the root mean square value of generalization errors.

  As can be seen from a comparison between FIG. 5A and FIG. 5B, the generalization error (root mean square value) is improved by using the MAP estimation method compared to when using the ML estimation method. I can see that Among them, the generalization error is greatly improved when the value of penalty β (n) is in the range of 1.0 to 3.0.

  FIGS. 6A and 6B show the measurement results of the dependency of the number of samples n in the penalty shot area. FIG. 6A shows the relationship between penalty β (n) and generalization error when n = 15. FIG. 6B shows penalty β (n) when n = 60. And the generalization error is shown. As shown in FIGS. 6 (A) and 6 (B), the optimum value of the penalty β (n) slightly increases as the number of samples n increases, but still β (n) = It can be seen that the best performance is obtained near 2.

  FIGS. 7A and 7B show the measurement results of the transition probability dependence of the penalty coefficient. FIG. 7A shows the relationship between penalty and generalization error when q2 = 0.001, and FIG. 7B shows the penalty and generalization error when q2 = 0.1. The relationship is shown. As shown in FIGS. 7 (A) and 7 (B), the optimum value of the penalty coefficient slightly increases as the transition probability q2 of the second group increases, but is still β (n). = The best performance is obtained around 2.0.

  8A, 8B, and 8C show the measurement results of the transition probability dependence of the penalty coefficient. FIG. 8A shows the relationship between the penalty and the generalization error when the transition magnitude σ2 of the second group is 0.001, and FIG. 8B shows the second group. FIG. 8C shows the relationship between the penalty and the generalization error when the transition magnitude σ2 of the second group is 0.005, and FIG. 8C shows that the transition magnitude σ2 of the second group is 0.01. The relationship between the penalty and the generalization error is shown. As shown in FIGS. 8A, 8B, and 8C, it can be seen that the best performance is obtained in the vicinity of β (n) = 2.

  From the above evaluation results, it can be seen that even if various simulation conditions are changed, consistently good performance can be obtained in the vicinity of β (n) = 2.0. Therefore, in this embodiment, β (n) is set to 1.0 or more and 3.0 or less, desirably β (n) is set to 1.0 or more and 2.0 or less. As described above, PL when β (n) = 2.0 is a likelihood corresponding to AIC.

  In this way, it is possible to determine by simulation that the optimum penalty β (n) value is almost constant regardless of the number of samples in the shot area, the second group model, etc. It is easy to set the penalty β (n) even in the device (unit). Therefore, after that, it is only necessary to make fine adjustments for each unit.

  In the present embodiment, the position detection method using the MAP estimation method described above is used to detect the position information of the sample shot area on the wafer W and perform EGA calculation. Based on the calculation result of the EGA, Based on the position information of the shot area calculated with accuracy, the exposure is performed on the wafer W by moving on the wafer stage WST, so that highly accurate exposure can be realized.

  In the above embodiment, the transition level of the parameter of the EGA model equation, that is, the priority of the transition is determined by the transition matrix T. However, this transition matrix T is limited to that shown in the above equation (6). I can't. However, in determining the priorities, it is desirable to increase the transition level as the order becomes higher if the coefficient includes even higher order components.

  In the above embodiment, the same transition matrix T is used for all wafers. However, the transition matrix T may be changed between the first wafer in the lot and the following wafers. For example, for the first wafer in a lot, a transition matrix is set so that the parameters can be easily updated as a whole, and for subsequent wafers, a transition matrix is set so that the parameters are not easily updated. Good.

In the above embodiment, the number of sample shot areas, that is, the number of effective samples is fixed, but these can be optimized simultaneously with the parameters. For example, in the wafer as shown in FIG. 2 as in the above embodiment, there are 2N wafer marks. From among the 2N number of wafer mark, a combination of when choosing a h number of wafer mark is as _2N C _h. Therefore, for each of the combinations, the expected value and sample variance of the overlay error of all shot regions are estimated, and the combination whose estimated value is good (minimum) is the number and arrangement of sample shots with the number of effective samples. You may make it do. Note that the expected value and sample variance of the overlay error for all shot areas need to find the maximum likelihood estimate for each coefficient in the selected model, but the maximum likelihood estimate for each coefficient in the model is Using the design position of the wafer mark and the standard deviation of the error distribution of the difference between the design position at the wafer mark and the actual measurement position, which is obtained empirically, the evaluation function using the least square method is minimized. It can be obtained from a so-called normal equation created based on a conditional expression.

  In the above embodiment, the number and arrangement of sample shots are obtained by the above-described method before performing the exposure operation. However, during the exposure operation, the maximum likelihood estimation method is performed, The number and arrangement may be optimized in real time.

  Further, in the exposure apparatus 100 of the above embodiment, in order to evaluate the overlay measurement result later, data such as the measurement result of the position information of the sample shot area and the value of the EGA parameter are collected as a data file. In many cases, the data file is stored in the storage device 47. If the causal relationship between the measurement result of the positional information of the sample shot area of a series of wafers and the value of the EGA parameter in the contents of this data file is analyzed, the exposure apparatus uses the MAP estimation as in this embodiment. It can be easily determined whether or not.

  In the above embodiment, whether or not each parameter value is a weighted average is determined only by likelihood estimation. However, it is recognized that the array shape of shot areas on the wafer is clearly changed. When it is, the parameter value of the model formula on the wafer can be forcibly set not to be the weighted average. This setting may be specified via an input device, which is a man-machine interface between the operator and the exposure apparatus 100, or is performed in a so-called process program including information on the process for the wafer. You may do it.

  In the above embodiment, the FIA type alignment sensor is used as the alignment detection system AS. However, as described above, the laser beam is irradiated to the alignment mark in the form of a dot on the wafer W and is diffracted by the mark. The present invention can also be applied to an LSA (Laser Step Alignment) type alignment sensor that detects a mark position using scattered light, or an alignment sensor that appropriately combines the alignment sensor and the FIA method. . In addition, for example, an alignment sensor that irradiates a mark on the surface to be detected with a coherent detection light and causes two diffracted lights (for example, the same order) generated from the mark to interfere with each other is used alone, or the FIA method, the LSA. Of course, the present invention can be applied to an alignment sensor appropriately combined with a method or the like.

  The alignment detection system may be an on-axis method (for example, a TTL (Through The Lens) method). In addition, the alignment detection system is not limited to the one that detects the alignment mark in a state where the alignment mark is almost stationary in the detection visual field of the alignment detection system. Relative movement may be used (for example, the aforementioned LSA system or homodyne LIA system). In the case where the detection light and the alignment mark are moved relative to each other, it is desirable that the relative movement direction is the same as the movement direction of the wafer stage WST when detecting each of the alignment marks.

Further, although the light source of the exposure apparatus to which the present invention is applied is a KrF excimer laser, an ArF excimer laser, or an F ₂ laser, other pulse laser light sources in the vacuum ultraviolet region may be used. In addition, as the illumination light for exposure, for example, a fiber doped with erbium (or both erbium and ytterbium), for example, an infrared or visible single wavelength laser beam oscillated from a DFB semiconductor laser or fiber laser. Harmonics that are amplified by an amplifier and wavelength-converted to ultraviolet light using a nonlinear optical crystal may be used.

  An illumination optical system, a projection optical system, and an alignment detection system AS composed of a plurality of lenses are incorporated in the exposure apparatus main body, optically adjusted, and a reticle stage and wafer stage made up of a large number of mechanical parts are arranged in the exposure apparatus main body. The exposure apparatus of the above-described embodiment can be manufactured by connecting the wiring and pipes to each other and further performing general adjustment (electrical adjustment, operation check, etc.). The exposure apparatus is preferably manufactured in a clean room where the temperature, cleanliness, etc. are controlled.

  In the above embodiment, the step-and-scan type projection exposure apparatus has been described. However, the present invention is not limited to the step-and-repeat type projection exposure apparatus, and other exposure apparatuses such as a proximity-type exposure apparatus. Needless to say, this can also be applied. The present invention can also be suitably applied to a step-and-stitch reduction projection exposure apparatus that combines a shot area and a shot area. The present invention can also be applied to a twin stage type exposure apparatus having two wafer stages. Of course, the present invention can also be applied to an exposure apparatus using a liquid immersion method.

  The present invention is not limited to an exposure apparatus for manufacturing a semiconductor, but is used for manufacturing a display including a liquid crystal display element. An exposure apparatus for transferring a device pattern onto a glass plate and a device used for manufacturing a thin film magnetic head. The present invention can also be applied to an exposure apparatus that transfers a pattern onto a ceramic wafer, an exposure apparatus used for manufacturing an image sensor (CCD, etc.), an organic EL, a micromachine, and a DNA chip. Further, in order to manufacture reticles or masks used in not only microdevices such as semiconductor elements but also light exposure apparatuses, EUV exposure apparatuses, X-ray exposure apparatuses, electron beam exposure apparatuses, etc., glass substrates or silicon wafers, etc. The present invention can also be applied to an exposure apparatus that transfers a circuit pattern.

  The position detection method according to the present invention is not limited to an exposure apparatus, and can be applied to any apparatus that needs to select and detect several marks from a plurality of marks formed on an object. Is possible.

  The semiconductor device includes a step of performing functional / performance design of the device, a step of manufacturing a reticle based on the design step, a step of manufacturing a wafer from a silicon material, and a reticle pattern by the lithography system and the exposure apparatus 100 of the above-described embodiment. Are transferred through a wafer, a device assembly step (including a dicing process, a bonding process, and a packaging process), an inspection step, and the like.

  The position detection method of the present invention is suitable for detecting position information for aligning an object. The exposure method of the present invention is suitable for a lithography process for manufacturing a semiconductor element, a liquid crystal display element, and the like.

It is a figure which shows schematically the structure of the exposure apparatus which concerns on one Embodiment of this invention. It is a figure which shows an example of arrangement | positioning of the shot area | region on a wafer, and the wafer mark attached to this. It is a flowchart which shows the process algorithm of CPU of the main control apparatus in the case of the exposure process in the exposure apparatus which concerns on one Embodiment of this invention. It is a flowchart which shows a wafer alignment process. FIG. 5A is a graph showing the relationship between the penalty when using the ML estimation method and the generalization error. FIG. 5B shows the penalty and the generalization error when using the MAP estimation method. It is a graph which shows the relationship. FIG. 6A is a graph showing the relationship between penalty and generalization error when the number of samples n = 15, and FIG. 6B shows the penalty and generalization error when the number of samples n = 60. It is a graph which shows a relationship. FIG. 7A is a graph showing the relationship between the penalty and the generalization error when the second group transition probability dependency q2 = 0.001, and FIG. 7B shows the transition probability of the second group. It is a graph which shows the relationship between penalty and generalization error in case of dependence q2 = 0.1. FIG. 8A is a graph showing the relationship between the penalty and the generalization error when the transition magnitude σ2 = 0.001 of the second group, and FIG. 8B shows the transition of the transition of the second group. FIG. 8C is a graph showing the relationship between the penalty and the generalization error when the magnitude σ2 = 0.005, and FIG. 8C shows the penalty and the generalization when the magnitude σ2 = 0.01 of the transition of the second group. It is a graph which shows the relationship with a conversion error.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 ... Illumination system, 15 ... Moving mirror, 16 ... Reticle interferometer, 17 ... Moving mirror, 18 ... Wafer interferometer, 19 ... Stage controller, 20 ... Main controller, 22 ... Reticle alignment detection system, 24 ... Wafer stage drive unit, 25 ... holder, 46 ... drive unit, 47 ... storage device, 100 ... exposure apparatus, AS ... alignment detection system, AX ... optical axis, the center of the C _p ... shot areas, IL ... illumination light, FM ... reference mark plate, MX _p, MY _p ... wafer X, Y mark, PL ... projection optical system, R ... reticle, RST ... reticle stage, SA _p ... shot area (divided area), W ... wafer (object), WST ... wafer stage .

Claims (10)

In a position detection method for detecting position information of a plurality of partitioned areas respectively arranged on a plurality of objects,
When calculating values of a plurality of parameters of a predetermined model that defines an array of the plurality of partition regions for each object, based on detection results of position information of at least some of the plurality of partition regions. Depending on the value of the predetermined evaluation criterion obtained, the value of at least a part of the plurality of parameters, the value of the parameter obtained only from the detection result, and the parameter obtained so far A position detection method comprising: determining a weight given to both based on both of the two values and changing the weight. In a position detection method for detecting position information of a plurality of partitioned areas respectively arranged on a plurality of objects,
When calculating values of a plurality of parameters of a predetermined model that defines an array of the plurality of partition regions for each object, based on detection results of position information of at least some of the plurality of partition regions. Depending on the value of the predetermined evaluation criterion obtained, the value of at least a part of the plurality of parameters is the value of the parameter obtained only from the detection result or includes the value of the parameter A position detection method comprising selecting whether to use a weighted average value of the parameter values obtained so far.   The position according to claim 2, wherein when a value of the parameter obtained only from the detection result is selected, a weight of the parameter value obtained before is set to 0. Detection method.   The position detection method according to claim 1, wherein the plurality of parameters defining the predetermined model are parameters orthogonalized to each other.   Based on the weighted average value of the parameter values obtained in the past and the value of the parameter obtained only from the detection result, the parameter values obtained so far including the value of the parameter are sequentially calculated. The position detection method according to claim 1, wherein a weighted average value is obtained. When performing the sequential calculation,
6. The position detection method according to claim 5, wherein a weight given to a weighted average value of parameter values obtained in the past is the number of the objects that contributed to the calculation of the weighted average value. When performing the sequential calculation,
The position detection method according to claim 5 or 6, wherein the weighted average value of the parameter values obtained in the past is multiplied by a forgetting factor for reducing the weight.   The position detection method according to claim 1, wherein the predetermined evaluation criterion is a likelihood given a penalty according to a degree of freedom of a parameter of the model.   The position detection method according to claim 8, wherein a set value of a penalty in the predetermined evaluation criterion is 1.0 or more and 3.0 or less. An exposure method for sequentially exposing a plurality of partitioned areas arranged on an object to form a predetermined pattern in each partitioned area,
Detecting the position information of the plurality of partitioned regions using the position detection method according to any one of claims 1 to 9;
An exposure method comprising: moving the object based on the detected position information to expose the partitioned areas.

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