JP4481100B2 - Charged particle beam exposure method - Google Patents

Description

  The present invention relates to a charged particle beam exposure method, and more particularly to a charged particle beam exposure method that suppresses a reduction in exposure margin due to a proximity effect.

  With recent miniaturization of LSIs, a desired pattern is exposed by directly drawing on a resist on a wafer or a mask with a charged particle beam, for example, an electron beam. In such charged particle beam exposure, it is known that the shape of the exposure and development pattern deviates from the design value due to the proximity effect due to the scattering of electrons generated when the resist is irradiated with the electron beam. As a method for correcting the proximity effect, it is common to use the following double Gaussian approximation formula indicating the accumulated energy distribution F (r) by the electron beam.

ここで、ｒは電子線入射点からの距離、ηは後方散乱比率、βｆは前方散乱長、βｂは後方散乱長であり、これらの係数は、レジストプロセスなどにより決定される。そして、第一項は前方散乱分を、第二項は後方散乱分をそれぞれ示す。実際のパターンの蓄積エネルギープロファイルは、上記式をパターンエリア内で積分することにより得られる誤差関数で表される。

Here, r is the distance from the electron beam incident point, η is the backscattering ratio, βf is the forward scattering length, and βb is the backscattering length, and these coefficients are determined by a resist process or the like. The first term indicates the forward scattering component, and the second term indicates the backward scattering component. The actual stored energy profile of the pattern is represented by an error function obtained by integrating the above equation within the pattern area.

  In the case of an electron beam exposure apparatus with an acceleration voltage of 50 kV or more in recent years, the forward scattering length is about 100 nm, whereas the backward scattering length is on the order of several tens of μm, and the forward scattering component gives energy to the pattern itself. In contrast, backscattering affects the pattern itself and surrounding patterns. That is, the influence of forward scattering is steep and the influence of backscattering spreads widely and gently. Therefore, a pattern is formed with the energy of the forward scattering term, and the backscattering can be handled as a background amount that raises the entire energy.

  It has been proposed to obtain the above-mentioned stored energy profile based on the area density and to correct the proximity effect by correcting the exposure amount. For example, it is described in Patent Document 1. In this method, on the assumption that a predetermined reference level width (for example, half-value width) of the stored energy profile corresponds to the pattern size, the exposure amount is corrected to match the design value. For example, in a region having a high area density, the exposure amount is reduced, and the width of the pattern to be exposed and developed is matched with the design value.

Furthermore, in the region where the area density is high due to the proximity effect, the accumulated energy due to back scattering tends to increase and the pattern width tends to be thicker. Conversely, in the region where the area density is low, the accumulated energy due to back scattering decreases and the pattern width becomes narrow. Tend to be. Paying attention to this point, it has been proposed to correct the proximity effect by changing the pattern width in accordance with the area density. For example, as shown in Patent Document 2.
JP 2001-52999 A JP 2000-323377 A

  However, in the method of correcting the exposure amount according to Patent Document 1, it is necessary to reduce the exposure amount in a region with a high area density, and as a result, the contrast at the boundary between the exposed region and the non-exposed region of the accumulated energy profile is poor, There is a problem that the exposure margin is low. In other words, due to variations in exposure dose and exposure sensitivity due to resist thickness, the pattern width greatly fluctuates even if the effective exposure dose slightly deviates from the optimum exposure dose, which is not practical.

  Further, in the method of shifting the pattern width according to Patent Document 2, since the pattern width is shifted depending only on the area density, not only the pattern that has a high area density of the pattern and requires proximity effect correction, but also is sufficient in nature. A pattern having a large exposure margin may be subjected to pattern width shift, leading to deterioration of the throughput of the exposure process. That is, simply shifting the pattern width depending only on the pattern area density is not an optimal method for preventing the exposure margin from deteriorating.

  SUMMARY OF THE INVENTION An object of the present invention is to provide a charged particle beam exposure method using proximity effect correction that can suppress exposure margin deterioration.

  To achieve the above object, according to a first aspect of the present invention, in a charged particle beam exposure method for exposing a resist layer to a plurality of patterns by irradiating a charged particle beam with a predetermined exposure amount, A correction step of extracting a pattern in which the inclination of the pattern edge position of the accumulated energy profile of the resist layer when exposed with an exposure amount of less than a predetermined reference value and correcting the pattern so as to reduce the size of the extracted pattern; A correction step of correcting the exposure amount of the pattern corrected pattern to an exposure amount corresponding to the desired pattern size based on the accumulated energy profile of the pattern corrected pattern, and the pattern based on the corrected exposure amount. And an exposure step of performing exposure with a corrected pattern size.

  In order to achieve the above object, according to a second aspect of the present invention, in a charged particle beam exposure method for exposing a resist layer to a plurality of patterns by irradiating a charged particle beam with a predetermined exposure amount, Based on the accumulated energy profile of the resist layer when exposed by the exposure amount, a first correction step of correcting the exposure amount of each pattern to an exposure amount that can correspond to a desired pattern size, and the corrected exposure amount A second correction step of extracting a pattern in which the slope of the pattern edge position of the stored energy profile when exposed is less than a predetermined reference value and correcting the pattern so as to reduce the size of the extracted pattern; and the pattern correction Based on the accumulated energy profile of the pattern, the exposure amount of the pattern corrected pattern is A third correction step for correcting the exposure amount to correspond to the desired pattern size, and an exposure step for performing exposure with the pattern size corrected by the exposure amount corrected in the first and third correction steps. It is characterized by having.

  In a preferred embodiment of the first or second aspect of the invention described above, in a preferred embodiment, in the correction step of correcting the exposure amount, exposure is performed such that a width of the accumulated energy profile at a predetermined exposure threshold level matches the desired pattern size. It is characterized by correcting the quantity.

  According to the first or second aspect of the present invention, by performing pattern correction and exposure amount correction on a pattern in which the inclination of the pattern edge position of the stored energy profile is less than a predetermined reference value, the stored energy is obtained. The inclination of the profile can be increased and the exposure margin can be increased.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. However, the technical scope of the present invention is not limited to these embodiments, but extends to the matters described in the claims and equivalents thereof.

  FIG. 1 is a diagram showing a stored energy profile in the present embodiment. In the figure, the horizontal axis corresponds to a region (a) with a high pattern density and a region (b) with only an isolated pattern and a low pattern density, and the vertical axis represents a resist layer when exposed with exposure doses D0 and D0 ′. Corresponds to the stored energy. The stored energy profile is represented by an error function obtained by area integration of the aforementioned stored energy distribution F (r). That is, in order to obtain the accumulated energy profile of a certain area, it is necessary to integrate the scattering amount F (r) from the surrounding area including the area.

  In the high density region (a), the patterns having the pattern width W0 are dense, and in the low density region (b), only an isolated pattern having the pattern width W0 exists. In the isolated pattern region (b), since there is no beam irradiation to the peripheral area, the contribution of backscattering from the peripheral area is very small, and the energy profile corresponding to the exposure dose D0 can be obtained as it is. The stored energy profile width W0 at the exposure threshold level Eth substantially matches the exposure pattern width W0, which is a design value. On the other hand, in the high density region (a), since there are many patterns around, the contribution of backscattering from the surrounding area becomes very large. When the exposure is performed with the exposure amount D0 ′, the backscattering contribution is αηD0 ′, which is added to the forward scattering of the exposure amount D0 ′ for each pattern as a background amount. Here, α is the area density, η is the ratio of backscattering, and 0 <η <1. In the example of FIG. 1, by setting the exposure amount D0 ′ (<D0) corrected in the high-density region (a), the width of the stored energy profile at the exposure threshold level Eth is an exposure pattern width W0 that is a design value. Try to match.

  FIG. 2 is a diagram showing another stored energy profile in the present embodiment. In this example, the pattern width W1 of the high-density region is large and the area density α1 is further increased. In this case, since the backscattering contribution becomes larger than that in the case of FIG. 1, the width of the stored energy profile at the exposure threshold Eth tends to increase. Therefore, in the example of FIG. 2, the exposure amount in the high-density region is set to a lower D1, so that the pattern width W1 at the exposure threshold Eth of the stored energy profile matches the exposure pattern width W1 of the design value.

  However, as is apparent from the stored energy profile of FIG. 2, the inclination of the profile at the pattern edge in the high density region is very small, the contrast is low, and the pattern width at the exposure threshold Eth varies greatly when the effective exposure varies. I can understand. On the other hand, in the isolated pattern, it can be understood that the inclination of the profile at the pattern edge is very large, the contrast thereof is high, and the pattern width W0 at the exposure threshold Eth hardly varies even if the effective exposure amount slightly varies.

  FIG. 3 is a diagram showing the pattern width with respect to the effective exposure amount of the high density region and the isolated pattern region. The horizontal axis corresponds to the effective exposure amount, and the vertical axis corresponds to the pattern width to be exposed and developed. As described with reference to the stored energy profile in FIG. 2, the pattern width of the isolated pattern region (b) has little variation with respect to the effective exposure amount on the horizontal axis, as indicated by the broken line. Accordingly, the effective exposure amount width Mb for obtaining the allowable range d0 centered on the desired pattern width W0 is wide. This width Mb is an exposure margin. On the other hand, the pattern width of the high-density region (a) varies greatly with respect to the effective exposure amount on the horizontal axis, as shown by the solid line. Accordingly, the width of the effective exposure amount for obtaining the allowable range d1 centered on the desired pattern width W1 is narrow. In addition, in this example, when the effective exposure amount is increased, the patterns are short-circuited, so that the exposure margin Ma is reduced accordingly. As described above, in the high-density region (a), the exposure margin is narrowed as the exposure amount D1 is corrected, and it is difficult to adapt to implementation on a practical production line.

  FIG. 4 is a flowchart of the electron beam exposure method in the present embodiment. The present embodiment can be applied to a charged particle beam exposure method, but the following description will be made using an electron beam as an example. 5, FIG. 6, FIG. 7, and FIG. 8 are diagrams for explaining each step of the flowchart. First, design data F1 having a plurality of pattern data is converted into exposure data F2 having a format that can be recognized by the electron beam exposure apparatus (S10). And as shown below, it correct | amends about the exposure pattern and exposure amount of exposure data.

  First, the exposure amount of each pattern is corrected based on the accumulated energy profile based on the reference exposure amount D0 so that the pattern width to be exposed and developed becomes the pattern width as designed (S12). FIG. 5 shows a stored energy profile when the exposure is performed with the reference exposure dose D0. In this profile example, the high-density area (a) and the isolated pattern area (low-density area) (b) are exposed with the same reference exposure amount D0. In this case, in the isolated pattern region (b), the width W0 (Eth = D0 / 2, half-value width W0) at the exposure threshold Eth of the stored energy profile matches the design value W0, that is, the exposure pattern width W0. In the high density region (a), the width W1 ′ at the profile threshold Eth is larger than the design value W1, that is, the exposure pattern width W1. This is because the influence of backscattering is large. Therefore, by correcting the exposure amount of the pattern in the high density region to D1 lower than the reference exposure amount D0, as shown in FIG. 6, the width W1 at the threshold value Eth of the stored energy profile matches the design value W1. . FIG. 6 is the same as FIG. 2. By correcting the exposure amount D1 in the high-density region (a) to be lower than the reference exposure amount D0, the pattern width W1 to be exposed / developed is matched with the design value W1. Yes.

  Next, an accumulated energy profile when exposure is performed with the corrected exposure amount D1 is obtained, and inclinations m0 and m1 of pattern edge positions of the profile are obtained, and a pattern having an inclination smaller than a reference value (for example, 1) of the inclination is obtained. Extract (S14). FIG. 6 shows a stored energy profile when the high-density area (a) is exposed with the corrected exposure dose D1 and the low-density area (b) is exposed with the reference exposure dose D0. In the isolated pattern region (b), the slope m0 = 10, which is large, whereas in the high density region (a), the slope m1 = 0.95, which is smaller than 1. Therefore, the pattern of the high-density region (a) in FIG. 6 is extracted by step S14. That is, a pattern with a low contrast of the stored energy profile and a low exposure margin is extracted.

  Therefore, in order to increase the exposure margin of the extracted pattern, a minus shift is performed so as to reduce the exposure pattern size of the extracted pattern (S16). FIG. 7 shows an accumulated energy profile when the exposure pattern size W1 ′ is reduced by δS from the design value pattern size W1. As the exposure pattern width is reduced to W1 ′ while leaving the exposure amount D1 in the high density region (a) as it is, the area density α2 (<α1) decreases, and the backscattering level decreases accordingly. . As a result, the pattern width W2 at the threshold Eth level is smaller than the design value W1.

  After reducing the area density of the high-density region (a) in this way, the pattern size at the threshold Eth level matches the design value based on the stored energy profile, as in the methods of FIGS. Then, the exposure amount is corrected (increased) (S18). FIG. 8 shows a stored energy profile when the exposure is performed with this corrected exposure amount. By increasing the exposure amount in the high density region (a) to D2 (> D1), the energy value of the accumulated energy profile is increased, and the pattern width W1 at the exposure threshold Eth matches the design value W1. Then, by making the exposure pattern width W1 ′ narrower than the design value W1, the area density α2 of the high-density region was lowered, and the energy level due to backscattering could be lowered. As a result, the slope m1 ′ of the stored energy profile at the exposure threshold Eth is sufficiently higher than 1, the contrast is increased, and the exposure margin is improved.

  FIG. 9 is a diagram showing an exposure margin in the exposure method of the present embodiment. As in FIG. 3, the horizontal axis represents the effective exposure amount, and the vertical axis represents the pattern width. According to the exposure method of the present embodiment, the exposure amount and the exposure pattern width of the exposure data are corrected, and the inclination (contrast) at the pattern edge of the stored energy profile is increased. Accordingly, as shown by the solid line in FIG. 9, the effective exposure width Ma (exposure margin) with respect to the allowable range d1 centered on the design value W1 in the high density region (a) is widened. As a result, the common exposure margin Mc overlapping the exposure margin Mb of the isolated pattern region is also widened. Therefore, the fluctuation range of the exposure / development pattern width can be reduced with respect to the fluctuation of the effective exposure amount, and the process is highly practical.

  Returning to FIG. 4, the exposure data F2C corrected as described above is given to the exposure apparatus, and exposure to the wafer or mask is executed (S20). Since the exposure data is corrected so as to increase the exposure margin, in the actual exposure process, exposure and development can be performed with a pattern width as designed even for a slight variation in the effective exposure amount.

  In the exposure method in the above embodiment, the inclination of the stored energy profile is checked for all patterns, and the pattern correction and the exposure amount correction are performed on the pattern having a low inclination. However, since the pattern that requires this pattern correction and exposure amount correction is a region having a high area density, in the pattern extraction step in step S14, referring to the area density map of the exposure region that has been obtained in advance, It is also possible to limit only the pattern of a region having a predetermined area density or higher to the extraction target, obtain the gradient of the stored energy profile for the pattern of the region, and extract a pattern having a gradient lower than the reference value. By doing so, the throughput of the extraction step S14 can be improved.

  Further, as a shift amount in the pattern correction step S16, a correction table having a shift amount according to the width of the pattern extracted in step S14 and the distance (adjacent distance) between the adjacent pattern and the inclination m1 of the profile of the extracted pattern. Is created in advance, and the shift amount is obtained with reference to the correction table, whereby the throughput of the exposure data conversion process can be improved.

  FIG. 10 is a chart showing an example of the correction table in the present embodiment. In each case where the pattern width 2 μm, 5 μm, 10 μm of the correction target in the vertical direction of the chart and the interval between adjacent patterns of the correction target pattern in the horizontal direction are 0.2 μm, 0.5 μm, 1.0 μm, 2.0 μm, The inclination reference value “1” or “0.8” of the profile to be extracted and the shift amounts “−20 nm”, “−30 nm”, and “−40 nm” are shown. When the pattern width is 5 μm and the distance between adjacent patterns is 0.2 μm, it is shown that the pattern width is reduced by −30 nm for a pattern with an inclination of 1 or less as “−30 nm / 1”.

  That is, if the pattern width to be corrected is less than a certain value, such as 2 μm, the pattern width is not negatively shifted. Further, when the pattern width to be corrected is 5 μm or more and the interval between adjacent patterns is narrow (0.2 μm to 0.5 μm), the pattern shift of −30 nm is applied to the pattern edge whose profile slope is 1 or less. Insert. Pattern shifts are not applied to pattern edges having a larger adjacent distance. When the correction target pattern width is 10 μm or more and the adjacent distance is narrow (0.2 μm to 0.5 μm), a pattern shift of −40 nm is added to the pattern edge whose profile slope is 1 or less. . When the correction target pattern width is 10 μm or more and the adjacent distance is slightly narrow (0.5 μm to 1.0 μm), a pattern edge of −20 nm is applied to a pattern edge having a profile inclination of 0.8 or less. Put a shift. No pattern shift is applied to the pattern edge having an adjacent distance longer than that.

  As described above, in the correction table of FIG. 10, the minus shift amount is increased as the pattern width to be corrected is larger and the interval between adjacent patterns is narrower. That is, the amount of minus shift is increased as the area density increases. Further, as the interval between adjacent patterns is wider, the minus shift amount is made smaller or zero shift. Then, the wider the interval between adjacent patterns, the lower the slope of the pattern correction target pattern edge, thereby limiting the number of correction target pattern edges. This is because if the distance to the adjacent pattern is wide, the possibility of short-circuiting with the adjacent pattern is low even if the pattern width is expanded due to the proximity effect. It is possible to limit the throughput of the data conversion process.

  Further, the pattern extraction step S14 and the pattern correction step S16 can be performed as follows. The slope m1 of the stored energy profile tends to be low when the area density α is high, the influence of backscattering is large, and the exposure amount is small. Even if the area density α is high, the slope is large if the exposure amount is high, while the slope is large if the area density α is low even if the exposure amount is low. Therefore, in the pattern extraction step S14, a correction target pattern is extracted according to the area density α1 and the exposure amount D1 in FIG. Further, in the pattern correction step S16, pattern correction is performed with reference to a correction table having a pattern shift amount according to the pattern width, the adjacent distance, the area density, and the exposure amount.

  In the above embodiment, after correcting the exposure amount in step S12, a pattern having a low slope of the stored energy profile at the corrected exposure amount, that is, a pattern having a low exposure margin is extracted, and pattern correction S16 and exposure amount correction are performed. S18 is performed. The present embodiment is not limited to this, and when exposure is performed with some exposure amount, a pattern with a small exposure margin is extracted based on the inclination at the pattern edge position of the stored energy profile at the exposure amount, Correction S16 and exposure correction S18 may be performed.

  As described above, according to the present embodiment, a pattern having a small exposure margin is subjected to a correction of a minus shift of the pattern width and an exposure amount correction to compensate for an insufficient exposure amount, thereby reducing the exposure margin. It is high. Therefore, it is a highly practical exposure method that is resistant to fluctuations in the effective exposure amount.

  The above embodiment is summarized as follows.

(Additional remark 1) In the charged particle beam exposure method which irradiates a charged particle beam by predetermined exposure amount, and exposes a resist layer to a some pattern,
A correction step of extracting a pattern in which the inclination of the pattern edge position of the accumulated energy profile of the resist layer when exposed with a predetermined exposure amount is less than a predetermined reference value, and correcting the pattern so as to reduce the size of the extracted pattern When,
Based on the accumulated energy profile of the pattern corrected pattern, a correction step of correcting the exposure amount of the pattern corrected pattern to an exposure amount that can correspond to the desired pattern size;
And an exposure step of performing exposure with the pattern size corrected with the corrected exposure amount.

  (Supplementary note 2) In the supplementary note 1, in the correction step of correcting the exposure amount, the charge amount is corrected so that a width of the accumulated energy profile at a predetermined exposure threshold level matches the desired pattern size. Particle beam exposure method.

  (Supplementary note 3) The charged particle beam exposure method according to supplementary note 1, wherein, in the correction step of pattern correction, the pattern is extracted from a pattern group in a region where the pattern area density is higher than a predetermined reference value.

  (Supplementary note 4) In the supplementary note 1, in the correction step of correcting the pattern, for a pattern whose distance from the adjacent pattern is the first distance, the reference value of the inclination is set to the first reference value, Charged particles characterized in that pattern extraction is performed with a second reference value lower than the first reference value for a pattern having a second distance longer than the first distance. Beam exposure method.

(Additional remark 5) In the charged particle beam exposure method which irradiates a charged particle beam with predetermined exposure amount, and exposes a resist layer to a some pattern,
A first correction step of correcting the exposure amount of each pattern to an exposure amount corresponding to a desired pattern size based on an accumulated energy profile of the resist layer when exposed by a reference exposure amount;
A second correction for extracting a pattern in which the inclination of the pattern edge position of the stored energy profile when exposed with the corrected exposure amount is less than a predetermined reference value, and correcting the pattern so as to reduce the size of the extracted pattern Process,
A third correction step of correcting the exposure amount of the pattern corrected pattern to an exposure amount corresponding to the desired pattern size based on the accumulated energy profile of the pattern corrected pattern;
A charged particle beam exposure method comprising: an exposure step of performing exposure with the pattern size corrected by the pattern correction by the exposure amount corrected in the first and third correction steps.

  (Additional remark 6) In additional remark 5, in the said 1st and 3rd correction process, it correct | amends to the exposure amount which the width | variety of the said stored energy profile in a predetermined exposure threshold level corresponds to the said desired pattern size, It is characterized by the above-mentioned. A charged particle beam exposure method.

  (Supplementary note 7) The charged particle beam exposure method according to supplementary note 5, wherein, in the second correction step, the pattern is extracted from a pattern group in a region where the area density of the pattern is higher than a predetermined reference value.

  (Additional remark 8) In additional remark 5, in the said 2nd correction process, with respect to the pattern whose distance with an adjacent pattern is a 1st distance, the reference value of the said inclination is made into the 1st reference value, and the said adjacent pattern and Charged particles characterized in that pattern extraction is performed with a second reference value lower than the first reference value for a pattern having a second distance longer than the first distance. Beam exposure method.

It is a figure which shows the stored energy profile in this Embodiment. It is a figure which shows another stored energy profile in this Embodiment. It is a figure which shows the pattern width with respect to the effective exposure amount of a high-density area | region and an isolated pattern area | region. It is a flowchart figure of the electron beam exposure method in this Embodiment. It is a figure explaining each process of a flowchart. It is a figure explaining each process of a flowchart. It is a figure explaining each process of a flowchart. It is a figure explaining each process of a flowchart. It is a figure which shows the exposure margin in the exposure method of this Embodiment. It is a figure which shows an example of the correction table in this Embodiment.

Explanation of symbols

W0, W1: exposure pattern width, D0: reference exposure amount, D1: corrected exposure amount

Claims (5)

In a charged particle beam exposure method of exposing a resist layer to a plurality of patterns by irradiating a charged particle beam with a predetermined exposure amount,
A correction step of extracting a pattern in which the inclination of the pattern edge position of the accumulated energy profile of the resist layer when exposed with a predetermined exposure amount is less than a predetermined reference value, and correcting the pattern so as to reduce the size of the extracted pattern When,
Based on the accumulated energy profile of the pattern corrected pattern, a correction step of correcting the exposure amount of the pattern corrected pattern to an exposure amount that can correspond to the desired pattern size;
And an exposure step of performing exposure with the pattern size corrected with the corrected exposure amount.   2. The charged particle beam exposure according to claim 1, wherein, in the correction step of correcting the exposure amount, the exposure amount is corrected so that a width of the accumulated energy profile at a predetermined exposure threshold level matches the desired pattern size. Method.   2. The charged particle beam exposure method according to claim 1, wherein, in the correction step of correcting the pattern, the pattern is extracted from a pattern group in a region where the area density of the pattern is higher than a predetermined reference value.   2. The correction process according to claim 1, wherein in the pattern correction process, for a pattern whose distance from an adjacent pattern is a first distance, the reference value of the inclination is set as a first reference value, and the distance from the adjacent pattern is A charged particle beam exposure method, wherein a pattern having a second distance longer than the first distance is extracted with a second reference value lower than the first reference value. . In a charged particle beam exposure method of exposing a resist layer to a plurality of patterns by irradiating a charged particle beam with a predetermined exposure amount,
A first correction step of correcting the exposure amount of each pattern to an exposure amount corresponding to a desired pattern size based on an accumulated energy profile of the resist layer when exposed by a reference exposure amount;
A second correction for extracting a pattern in which the inclination of the pattern edge position of the stored energy profile when exposed with the corrected exposure amount is less than a predetermined reference value, and correcting the pattern so as to reduce the size of the extracted pattern Process,
A third correction step of correcting the exposure amount of the pattern corrected pattern to an exposure amount corresponding to the desired pattern size based on the accumulated energy profile of the pattern corrected pattern;
A charged particle beam exposure method comprising: an exposure step of performing exposure with the pattern size corrected by the pattern correction by the exposure amount corrected in the first and third correction steps.

Images