JP3583622B2 - Resist pattern prediction method - Google Patents

Description

【００２１】
最後に、スライスレベルでの線幅を抽出する（ステップＳ１０）。
図２（ａ）に、本実施形態方法によりシミュレーションした、０．２１２５μｍの１：１のラインアンドスペースの結果を示す。図２（ｂ）に従来方法での結果も示すが、本実施形態の方法ではデフォーカス時にも良く実験結果と一致しているのが分かる。
【００２２】
このように本実施形態では、光学像の傾きに応じて光学像への変調のかけ方を変えることにより、デフォーカス時やパターンピッチを変えた場合にも高精度なシミュレーションを行うことができ、露光後のレジストパターン寸法を高精度に求めることが可能となる。しかも、光学像の変調の方法として、変調のパラメータを指数型減衰関数の減衰指標と係数に限定し、指数型減衰関数との畳み込み積分を行うようにしているので、シミュレーションのための計算が数学的にも扱い易く簡易になる利点がある。
【００２３】
なお、ウェハ上に形成される光学像の勾配とプロセスファクタΔＬ及びエッジ光強度シフトΔＰとの関係は予め求めておけば、シミュレーションの際に計算する必要はない。このため、上記のように光学像の傾きに応じて光学像への変調のかけ方を変えるようにしても、計算量の増加は極めて少なくでき、十分高速な計算スピードを維持できる。
【００２４】
（第２の実施形態）
図３は、本発明の第２の実施形態に係わるレジストパターン予測方法を説明するためのもので、特に第１の実施形態におけるステップＳ４を具体的に示すフローチャートである。
【００２５】
まず、異なるパターンサイズ及びパターンピッチの複数のマスクパターンを用意する。具体的には、種々のパターンサイズとして例えば ０．１８１２５μｍ〜０．２５μｍまでのパターンサイズ、種々のパターンピッチとして例えばライン：スペース＝１：１０の入ったマスクを準備する（ステップＳ１１）。
【００２６】
次いで、処理すべきパターンサイズ，パターンピッチ及び露光装置のデフォーカス値を設定し、そのパターンの露光を露光量を種々変えて行う（ステップＳ１２）。例えば、Ｗｏ ＝０．２５μｍのサイズでライン：スペース＝１：１のパターンに対して、露光装置のデフォーカスを０μｍと設定し、露光量をＥ＝１０ｍＪ／ｃｍ^２ 〜２０ｍＪ／ｃｍ^２ まで１ｍＪ／ｃｍ^２ 刻みに設定して露光を行う。
【００２７】
次いで、露光されたパターンに対するレジスト線幅を、例えばＳＥＭ等の測定装置で測定し、レジスト線幅の露光量依存性を測定する（ステップＳ１３）。その結果の例を、図４に示す。そして図４から、所望寸法（例えばマスクの設計寸法）Ｗｏ に仕上げるのに必要な露光量Ｅｅｘｐ を求める。さらに図４から、所望寸法近傍での線幅変動に対する必要露光量の変化率δｅｘｐ を求める（ステップＳ１４）。ここで、δｅｘｐ は次式で定義される。
【００２８】
Ｐｅｘｐ ＝ ｌｏｇ_１０Ｅｅｘｐ
δｅｘｐ ＝−ｄＰｅｘｐ ／ｄＷ
次いで、対象となるパターンに対する光学像Ｉｏ（ｘ） を計算する（ステップＳ１５）。次いで、光学像での所望寸法近傍での勾配δｃａｌｏを求める（ステップＳ１６）。但し、δｃａｌｏは次式で定義される。
【００２９】
δｃａｌｏ＝ｄ ｌｏｇ_１０Ｉｏ ／ｄＷ
次いで、適当なΔＬを与える（ステップＳ１７）。次いで、ΔＰ＝１として、次式のように指数型減衰関数と光学像Ｉｏ との畳み込み積分を実行する（ステップＳ１８）。
【００３０】
【数２】

【００３１】
次いで、畳み込み積分Ｉの所望寸法近傍での勾配δｃａｌ を求める（ステップＳ１９）。但し、δｃａｌ は次式で定義される。
δｃａｌ ＝ｄ ｌｏｇ_１０Ｉ／ｄＷ
次いで、δｅｘｐ とδｃａｌ との差が適当な誤差値ε以内に収まっているかの判定を行う（ステップＳ２０）。即ち、次式が成立するかどうかである。
【００３２】
｜δｅｘｐ −δｃａｌ ｜＜ε
上式が成り立っていれば次のステップＳ２１へ進み、そうでなければステップＳ１７に戻り、再度ΔＬを設定し計算をやり直し、上式が成り立つまで繰り返す。ステップＳ２１では、所定寸法での畳み込み積分の値Ｉｃａｌ を用いて次式に従ってΔＰを求める。
【００３３】
Ｐｃａｌ ＝ ｌｏｇ_１０Ｉｃａｌ
ΔＰ＝Ｐｅｘｐ −Ｐｃａｌ
次いで、全てのデフォーカス，パターンサイズ，パターンピッチで上記操作を行ったか否かを判定し、行っていない場合はステップＳ１２に戻り、パターンサイズ，パターンピッチ及び露光装置のデフォーカス値を再設定する（ステップＳ２２）。即ち、上記のステップＳ１２〜Ｓ２１を、デフォーカス，パターンサイズを変えて繰り返し行い、最終的にδｃａｌｏとΔＬ、δｃａｌｏとΔＰとの関係を求める（ステップＳ２３）。図５（ａ）（ｂ）にその結果を示す。この図からそれぞれの関係を求めると、次式のようになる。
【００３４】
ΔＬ＝６４．５３６δｃａｌｏ−８０．４７６
ΔＰ＝−０．０１７δｃａｌｏ＋０．８０９２
これらの関係式を用いて第１の実施形態によりシミュレーションを行ったところ、極めて高精度なレジストパターン寸法の予測を行うことができた。なお、図５（ａ）（ｂ）に示す関係は、式として入力してもよいし、様々な値のδｃａｌｏに対するΔＬ，ΔＰの値をメモリに記憶させたテーブルを用いてもよい。
【００３５】
（第３の実施形態）
図６を用いて、本発明の第３の実施形態を説明する。
第２の実施形態では、光学像の勾配とΔＬ，ΔＰとの関係を求める際にパターンピッチは固定していたが、パターンピッチが異なるとこれらの関係も変わることがある。そこで本実施形態では、パターンピッチを様々に変えて第２の実施形態の操作を行い、パターンピッチ毎にδｃａｌｏとΔＬ、δｃａｌｏとΔＰとの関係を求めた。その結果をまとめると、図６のようになった。なお、図中の ｐｉｔｃｈ／ｗｄ は規格化寸法であり、例えばレジストＡの ｐｉｔｃｈ／ｗｄ＝２は１：１のラインアンドスペース、ｐｉｔｃｈ／ｗｄ＝２．５は１：１．５のラインアンドスペースを示している。
【００３６】
このように、パターンピッチ毎に関係が異なっている場合には、ピッチ毎に用いる関係式を変えて予測を行う。また、関係式の求まっていないピッチに関しては外挿又は内挿することによって関係式を求めればよい。こうして求めた関係式を用いて第１の実施形態と同様にシミュレーションを行ったところ、より高精度な予測を行うことができた。そして、ロジック回路のゲートパターンであっても、十分精度良い予測を行うことができた。
【００３７】
なお、本発明は上述した各実施形態に限定されるものではなく、その要旨を逸脱しない範囲で、種々変形して実施することができる。実施形態では、光学像に変調をかける手法として、指数型減衰関数との畳み込み積分を行うようにしたが、必ずしもこれに限らず他の手法を用いてもよい。例えば、重み付けが不要な場合は、定数関数による平均化操作を行うようにしてもよい。
【００３８】
また、上述した実施形態において記載した手法は、コンピュータに実行させることのできるプログラムとして、例えば磁気ディスク（フロッピーディスク，ハードディスク等）、光デイスク（ＣＤ−ＲＯＭ，ＤＶＤ等）、半導体メモリなどの記録媒体に書き込んで各種装置に適用したり、通信媒体により伝送して各種装置に適用することも可能である。本発明を実現するコンピュータは、記録媒体に記録されたプログラムを読み込み、このプログラムによって動作が制御されることにより、上述した処理を実行するものであればよい。
【００３９】
【発明の効果】
以上詳述したように本発明によれば、光学像の傾きに応じて光学像への変調のかけ方を変えることにより、デフォーカス時やパターンピッチを変えた場合にも高精度なシミュレーションを行うことができ、簡易なシミュレーションモデルでありながら、デフォーカス時までの良い予測精度が得られる。
【図面の簡単な説明】
【図１】第１の実施形態に係わるレジストパターン予測方法を説明するためのフローチャート。
【図２】レジスト線幅のＥＤ−ｔｒｅｅを示す図。
【図３】第２の実施形態に係わるレジストパターン予測方法の要部を説明するためのフローチャート。
【図４】レジスト線幅の露光量依存性を示す図。
【図５】第２の実施形態におけるδｃａｌｏとΔＬ及びΔＰとの相関を示す図。
【図６】第３の実施形態におけるδｃａｌｏとΔＬ及びΔＰとの相関に対するレジスト及びパターンピッチ依存性を示す図。
【図７】従来のレジストパターン予測方法を示すフローチャート。
【符号の説明】
Ｓ１…マスクパターン及び露光条件の入力ステップ
Ｓ２…線幅測定位置及び所望寸法の入力ステップ（第１の工程）
Ｓ３…スライスレベルの入力ステップ
Ｓ４…光学像の勾配とΔＬとの関係式の入力ステップ（第２の工程）
Ｓ５…光学像の勾配とΔＰとの関係式の入力ステップ（第２の工程）
Ｓ６…光学像の計算ステップ（第３の工程）
Ｓ７…光学像の勾配を求めるステップ（第４の工程）
Ｓ８…ΔＬ，ΔＰの算出ステップ（第５の工程）
Ｓ９…光学像の畳み込み積分を行うステップ（第６の工程）
Ｓ１０…スライスレベルでの線幅抽出ステップ（第７の工程）[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a lithography technique for semiconductors, and more particularly, to a resist pattern prediction method for predicting a dimension of a resist pattern obtained by transferring a mask pattern using an exposure apparatus. Further, the present invention relates to a recording medium storing a program for realizing the resist pattern prediction method by a computer.
[0002]
[Prior art]
In recent years, the degree of integration of LSIs has been increasing exponentially, and accordingly, design rules for wiring and the like inside the LSIs are becoming smaller and smaller. For example, the exposure wavelength is shortened from i-line (λ = 365 nm) to Kr excimer laser (λ = 248 nm), and the lens of the exposure apparatus is also increased in diameter (increased numerical aperture) to improve the resolution. .
[0003]
However, higher resolution by shortening the exposure wavelength and increasing the numerical aperture of the lens cannot keep up with the decrease in design rules. Therefore, prediction of a resist pattern after exposure by simulation has become increasingly important. For example, when a complicated device pattern is to be formed, a desired pattern shape and pattern size cannot be obtained due to an optical proximity effect. In this case, the mask pattern must be corrected in advance by an amount that allows for the proximity effect. In order to obtain this correction with high accuracy, a simulation method that can predict the dimension of the resist pattern with high accuracy is required.
[0004]
Various simulation methods have been proposed so far, from a method using a strict model to a simple method, but the strict model has a long calculation time and is not practical. A simple method is shown in FIG. 7 (Japanese Patent Application No. 8-148408). In this method, after inputting a mask pattern and exposure conditions, a desired resist dimension of a line width measurement position, and a slice level, a process factor ΔL is set. Then, calculation of an optical image for the mask pattern is performed, convolution integration of the obtained optical image and an exponential decay function using ΔL is performed, and a line width at a slice level is extracted, thereby performing high-speed simulation. be able to.
[0005]
However, this type of method has the following problems. That is, the example of FIG. 7 simulates the resist process by blurring the optical image by convolution integration of the optical image and the Gaussian function. Although the calculation speed is high, the accuracy is not very good. FIG. 2B shows the result of 0.2125 μm 1: 1 line and space. As can be seen from the figure, the best focus shows a good match, but the defocusing shows a considerable difference from the experimental results. Thus, with the conventional simple method, good prediction accuracy up to the time of defocus cannot be obtained.
[0006]
[Problems to be solved by the invention]
As described above, in the simple simulation model for resist pattern prediction as proposed in Japanese Patent Application No. 8-148408, the calculation speed is high, but good prediction accuracy until defocusing is obtained. There was no problem.
[0007]
The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a resist pattern predicting method capable of obtaining accurate prediction accuracy until defocusing while using a simple simulation model. It is in.
Another object of the present invention is to provide a recording medium storing a program for realizing the above-described method of predicting a resist pattern by a computer.
[0008]
[Means for Solving the Problems]
(Constitution)
In order to solve the above problems, the present invention employs the following configuration.
That is, the present invention relates to a resist pattern predicting method for predicting a dimension of a resist pattern formed by transferring a mask pattern onto a resist on a wafer using a projection exposure apparatus. A second step of setting a relationship between a gradient of an optical image formed on the wafer, a process factor, and an edge light intensity shift; and a mask pattern on the wafer by the projection exposure apparatus. A third step of calculating and calculating an optical image obtained by projecting the optical image on the basis of the optical image obtained in the third step. A fourth step of determining the gradient of the optical image to be processed, and a process factor and an edge light intensity based on the relationship set in the second step based on the gradient determined in the fourth step. A fifth step of obtaining a shift, a sixth step of modulating the optical image in accordance with the process factor and the edge light intensity shift obtained in the fifth step, and a modulation of the sixth step. And extracting a size of the resist pattern from the obtained optical image.
[0009]
Here, preferred embodiments of the present invention include the following.
(1) When modulating in the sixth step, convolution integration of the optical image with an exponential decay function is performed.
(2) Using the process factor obtained in the fifth step as the attenuation index of the exponential decay function, and selecting the edge light intensity shift obtained in the fifth step as the coefficient of the exponential decay function.
[0010]
(3) As a second step, a plurality of mask patterns having different pattern sizes and pattern pitches are prepared, and these mask patterns are transferred onto a resist on a wafer with different defocus and exposure amounts by a projection exposure apparatus, and are transferred. The measured pattern is measured to calculate an appropriate exposure amount and a change in exposure amount necessary to change the unit line width for each of the pattern size, pattern pitch, and defocus. Calculate the corresponding optical image of the mask pattern, determine the gradient of the obtained optical image, modulate the optical image by performing a convolution integral of the obtained optical image and the exponential decay function, and modulate the modulated optical image. The appropriate exposure and the change in exposure required to change the unit line width are determined from the optical image, and the calculated appropriate exposure and the calculated An index is set so that the proper exposure amount has a correlation, and the change in the exposure amount required to change the determined unit line width and the change in the exposure amount required to change the calculated unit line width have a correlation. Determining the mold decay function.
[0011]
(4) The process factor is a linear function of the gradient of the optical image.
(5) The edge light intensity shift is set to one number of the gradient of the optical image.
(6) To change the functional relationship between the process factor and the gradient of the optical image for each pattern pitch.
(7) The functional relationship between the edge light intensity shift and the gradient of the optical image, which should be changed for each pattern pitch.
[0012]
Further, the present invention is a computer-readable recording medium storing a program for estimating a dimension of a resist pattern formed by transferring a mask pattern onto a resist on a wafer using a projection exposure apparatus, A first procedure for setting a position and a desired dimension of the resist pattern to be predicted, and a second procedure for setting a relationship between a gradient of an optical image formed on the wafer, a process factor, and an edge light intensity shift. A third procedure for calculating and obtaining an optical image obtained by projecting the mask pattern onto the wafer by the projection exposure apparatus, and a first procedure based on the optical image obtained in the third procedure. A fourth procedure for obtaining the gradient of the optical image corresponding to the desired dimension at the dimension prediction position set in the procedure, and a second procedure for obtaining the gradient based on the gradient obtained in the fourth procedure. A fifth procedure for obtaining a process factor and an edge light intensity shift from the relationship set in the procedure, and a sixth procedure for modulating the optical image in accordance with the process factor and the edge light intensity shift obtained in the fifth procedure. And a seventh procedure for extracting the size of the resist pattern from the optical image modulated in the sixth procedure.
[0013]
(Action)
According to the present invention, the relationship between the gradient of the optical image formed on the wafer, the process factor, and the edge light intensity shift is set in advance, and the process factor and the edge light intensity are determined based on the relationship and the gradient of the optical image. The shift is newly obtained, and the optical image is modulated according to the obtained process factor and edge light intensity shift. Here, since the process factor includes information on the pattern pitch and the edge light intensity includes information on the defocus, the optical image is modulated depending on the defocus and the pattern pitch. Therefore, a highly accurate simulation can be performed even at the time of defocusing or when the pattern pitch is changed, and the resist pattern dimensions after exposure can be obtained with high accuracy.
[0014]
If the relationship between the gradient of the optical image formed on the wafer, the process factor, and the edge light intensity shift is obtained in advance, there is no need to calculate the relationship at the time of simulation. For this reason, even if the manner of modulating the optical image is changed according to the inclination of the optical image as described above, the increase in the amount of calculation can be extremely small, and a sufficiently high calculation speed can be maintained. That is, it is possible to obtain a high-precision prediction accuracy up to the time of defocusing at high speed with a simple simulation model.
[0015]
In addition, by performing convolution integration with an exponential decay function as a method of modulating an optical image, it is mathematically easy to handle and easy to calculate. Furthermore, by limiting the parameters of the modulation of the optical image to the decay index and the coefficient of the exponential decay function, the calculation becomes even easier.
[0016]
Further, by obtaining a method of applying a modulation to an optical image from an experimental value, it is possible to more accurately predict a resist pattern. By making the process factor and the edge light intensity shift a linear function of the gradient of the optical image, the relational expression can be simplified when determining how to apply the modulation to the optical image from the experimental values, making the calculation easier. It becomes possible to. Further, by changing the relational expression for each pitch, it is possible to further improve the accuracy.
[0017]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, the present invention will be described in detail with reference to the illustrated embodiments.
(1st Embodiment)
FIG. 1 is a flowchart for explaining a resist pattern prediction method according to the first embodiment of the present invention. The method according to the present embodiment is realized by a computer that reads a program recorded on a recording medium such as a magnetic disk and controls the operation of the program.
[0018]
First, a mask pattern for predicting a resist dimension (line width) and an exposure condition are input (step S1). Next, the coordinates of the position where the size prediction is to be performed and the desired resist size are input (step S2). At this time, there may be a plurality of positions where the line width is predicted. Next, a light intensity level (or slice level) corresponding to the exposure amount at the time of exposure is input (step S3). Next, a relational expression or a table between the gradient of the optical image and the process factor ΔL is input (step S4). Further, a relational expression or a table between the gradient of the optical image and the edge light intensity shift ΔP is input (step S5). Next, the optical image Io (x, y) for the given mask pattern is calculated (step S6). The order of steps S2 to S6 is not limited to the above and can be changed as appropriate.
[0019]
Next, based on the optical image Io calculated in step S6, the gradient of the optical image at the position corresponding to the desired dimension at the line width prediction position is obtained (step S7). Next, ΔL and ΔP are obtained from the obtained gradient of the optical image (step S8). Next, as shown in the following equation, convolution integration of the calculated optical image and an exponential decay function using ΔL and ΔP is performed (step S9).
[0020]
(Equation 1)

[0021]
Finally, the line width at the slice level is extracted (step S10).
FIG. 2A shows the result of 1: 1 line and space of 0.2125 μm simulated by the method of the present embodiment. FIG. 2B also shows the result of the conventional method, and it can be seen that the method of the present embodiment is in good agreement with the experimental result even at the time of defocusing.
[0022]
As described above, in the present embodiment, by changing the modulation method on the optical image in accordance with the inclination of the optical image, a highly accurate simulation can be performed even at the time of defocusing or changing the pattern pitch. The resist pattern dimensions after exposure can be obtained with high accuracy. Moreover, as a method of modulating the optical image, the parameters of the modulation are limited to the attenuation index and the coefficient of the exponential decay function, and convolution integration with the exponential decay function is performed. There is an advantage that it is easy to handle and simple.
[0023]
If the relationship between the gradient of the optical image formed on the wafer, the process factor ΔL, and the edge light intensity shift ΔP is obtained in advance, it is not necessary to calculate the relationship at the time of simulation. For this reason, even if the manner of modulating the optical image is changed according to the inclination of the optical image as described above, the increase in the amount of calculation can be extremely small, and a sufficiently high calculation speed can be maintained.
[0024]
(Second embodiment)
FIG. 3 is a flowchart for explaining a resist pattern prediction method according to the second embodiment of the present invention, and is a flowchart specifically showing step S4 in the first embodiment.
[0025]
First, a plurality of mask patterns having different pattern sizes and pattern pitches are prepared. More specifically, a mask having, for example, a pattern size of 0.18125 μm to 0.25 μm as various pattern sizes and a line: space = 1: 10 as various pattern pitches is prepared (step S11).
[0026]
Next, the size of the pattern to be processed, the pattern pitch, and the defocus value of the exposure device are set, and the pattern is exposed by changing the exposure amount in various ways (step S12). For example, Wo = 0.25 [mu] m in size line: space = 1: for one pattern, the defocus of the exposure apparatus is set to 0 .mu.m, the exposure amount to ^{E = 10mJ / cm 2 ~20mJ /} cm 2 1mJ The exposure is performed at a setting of / cm ² .
[0027]
Next, the resist line width for the exposed pattern is measured by, for example, a measuring device such as an SEM, and the exposure amount dependency of the resist line width is measured (step S13). FIG. 4 shows an example of the result. Then, from FIG. 4, an exposure amount Eexp required for finishing to a desired size (for example, a mask design size) Wo is obtained. Further, from FIG. 4, a change rate δexp of the required exposure amount with respect to the line width fluctuation near the desired dimension is obtained (step S14). Here, δexp is defined by the following equation.
[0028]
Pexp = log ₁₀ Eexp
δexp = −dPexp / dW
Next, the optical image Io (x) for the target pattern is calculated (step S15). Next, a gradient δcalo in the vicinity of a desired dimension in the optical image is obtained (step S16). Here, δcalo is defined by the following equation.
[0029]
δcalo = d log ₁₀ Io / dW
Next, an appropriate ΔL is given (step S17). Next, assuming that ΔP = 1, the convolution integral of the exponential decay function and the optical image Io is executed as in the following equation (step S18).
[0030]
(Equation 2)

[0031]
Next, a gradient δcal near the desired dimension of the convolution integral I is obtained (step S19). Here, δcal is defined by the following equation.
δcal = d log ₁₀ I / dW
Next, it is determined whether or not the difference between δexp and δcal is within an appropriate error value ε (step S20). That is, whether or not the following equation is satisfied.
[0032]
| Δexp -δcal | <ε
If the above equation holds, the process proceeds to the next step S21, otherwise, returns to step S17, sets ΔL again, repeats the calculation, and repeats until the above equation holds. In step S21, ΔP is obtained according to the following equation using the value Ical of the convolution integral in a predetermined dimension.
[0033]
Pcal = log ₁₀ Ical
ΔP = Pexp−Pcal
Next, it is determined whether or not the above operation has been performed for all defocus, pattern size, and pattern pitch. If not, the process returns to step S12 to reset the pattern size, pattern pitch, and defocus value of the exposure apparatus. (Step S22). That is, the above-described steps S12 to S21 are repeatedly performed while changing the defocus and the pattern size, and finally, the relationship between δcalo and ΔL and between δcalo and ΔP are obtained (step S23). FIGS. 5A and 5B show the results. When the respective relationships are obtained from this figure, the following equations are obtained.
[0034]
ΔL = 64.536δcalo−80.476
ΔP = −0.017δcalo + 0.8092
When a simulation was performed according to the first embodiment using these relational expressions, it was possible to predict the resist pattern dimensions with extremely high accuracy. The relationships shown in FIGS. 5A and 5B may be input as equations, or a table in which the values of ΔL and ΔP for various values of δcalo are stored in a memory may be used.
[0035]
(Third embodiment)
A third embodiment of the present invention will be described with reference to FIG.
In the second embodiment, the pattern pitch is fixed when obtaining the relationship between the gradient of the optical image and ΔL, ΔP. However, if the pattern pitch is different, these relationships may change. Therefore, in the present embodiment, the operation of the second embodiment is performed by changing the pattern pitch variously, and the relationship between δcalo and ΔL and the relationship between δcalo and ΔP are obtained for each pattern pitch. The results are summarized in FIG. In the drawing, pitch / wd is a standardized dimension. For example, pitch / wd = 2 of resist A is 1: 1 line and space, and pitch / wd = 2.5 is 1: 1.5 line and space. Is shown.
[0036]
As described above, when the relationship differs for each pattern pitch, the prediction is performed by changing the relational expression used for each pitch. For a pitch for which a relational expression has not been determined, the relational expression may be obtained by extrapolation or interpolation. A simulation was performed in the same manner as in the first embodiment using the relational expression thus obtained, and a more accurate prediction was able to be performed. And even with the gate pattern of the logic circuit, it was possible to make a sufficiently accurate prediction.
[0037]
The present invention is not limited to the above-described embodiments, and can be implemented with various modifications without departing from the scope of the invention. In the embodiment, as a method of modulating the optical image, convolution integration with an exponential decay function is performed. However, the present invention is not limited to this, and another method may be used. For example, when weighting is unnecessary, an averaging operation using a constant function may be performed.
[0038]
In addition, the method described in the above-described embodiment includes, as programs that can be executed by a computer, recording media such as a magnetic disk (floppy disk, hard disk, etc.), an optical disk (CD-ROM, DVD, etc.), a semiconductor memory And can be applied to various devices, or transmitted by a communication medium and applied to various devices. A computer that implements the present invention may read the program recorded on a recording medium, and may execute the above-described processing by controlling the operation of the program.
[0039]
【The invention's effect】
As described above in detail, according to the present invention, a highly accurate simulation is performed even at the time of defocus or when the pattern pitch is changed by changing the modulation method on the optical image according to the inclination of the optical image. This makes it possible to obtain a good prediction accuracy up to the time of defocusing while using a simple simulation model.
[Brief description of the drawings]
FIG. 1 is a flowchart for explaining a resist pattern prediction method according to a first embodiment.
FIG. 2 is a diagram showing an ED-tree of a resist line width.
FIG. 3 is a flowchart illustrating a main part of a method for estimating a resist pattern according to a second embodiment;
FIG. 4 is a view showing the exposure amount dependency of a resist line width.
FIG. 5 is a diagram showing a correlation between δcalo and ΔL and ΔP in the second embodiment.
FIG. 6 is a view showing the resist and pattern pitch dependence on the correlation between δcalo and ΔL and ΔP in the third embodiment.
FIG. 7 is a flowchart showing a conventional resist pattern prediction method.
[Explanation of symbols]
S1 ... Input step of mask pattern and exposure condition S2 ... Input step of line width measurement position and desired dimension (first step)
S3: Slice level input step S4: Input step of a relational expression between the gradient of the optical image and ΔL (second step)
S5: Step of inputting a relational expression between the gradient of the optical image and ΔP (second step)
S6: Optical image calculation step (third step)
S7: Step of obtaining gradient of optical image (fourth step)
S8: ΔL, ΔP calculation step (fifth step)
S9: Step of performing convolution integration of the optical image (sixth step)
S10: Line width extraction step at slice level (seventh step)

Claims (6)

In a resist pattern prediction method for predicting dimensions of a resist pattern formed by transferring a mask pattern onto a resist on a wafer using a projection exposure apparatus,
A first step of setting a position where a dimension of the resist pattern is to be predicted and a desired dimension, and a second step of setting a relationship between a gradient of an optical image formed on the wafer, a process factor, and an edge light intensity shift A third step of calculating and calculating an optical image obtained by projecting the mask pattern onto the wafer by the projection exposure apparatus; and a first step based on the optical image obtained in the third step. A fourth step of obtaining a gradient of the optical image corresponding to a desired dimension at the dimension prediction position set in the step, and a process based on the relationship set in the second step based on the gradient obtained in the fourth step. A fifth step of obtaining a factor and an edge light intensity shift; a sixth step of modulating the optical image according to the process factor and the edge light intensity shift obtained in the fifth step; Process Resist pattern prediction method, which comprises an optical image that has been subjected to modulation and a seventh step of extracting the dimensions of the resist pattern. When modulating in the sixth step, convolution integration of the optical image with an exponential decay function is performed, and the process factor obtained in the fifth step is taken as an attenuation index of the exponential decay function, 2. The method according to claim 1, wherein the edge light intensity shift obtained in the fifth step is selected as a coefficient of the exponential decay function. As a second step, a plurality of mask patterns having different pattern sizes and pattern pitches are prepared, and these mask patterns are respectively transferred to a resist on a wafer with different defocus and exposure amounts by a projection exposure apparatus. Is measured to calculate an appropriate exposure amount and a change in exposure amount required to change the unit line width for each of the pattern size, pattern pitch, and defocus, and calculate the mask pattern for each of the pattern size, pattern pitch, and defocus. Calculate the corresponding optical image, determine the gradient of the obtained optical image, modulate the optical image by performing convolution integration of the obtained optical image and the exponential decay function, and from this modulated optical image The appropriate exposure and the change in exposure required to vary the unit line width are determined, and the determined appropriate exposure and the calculated appropriate exposure are calculated. Exponential decay so that the amount of light has a correlation, and the change in exposure required to fluctuate the determined unit line width and the change in exposure required to fluctuate the calculated unit line width have a correlation. 3. The method according to claim 2, wherein the function is determined. 4. The method according to claim 3, wherein the process factor and the edge light intensity shift are each a linear function of the gradient of the optical image. 5. The method according to claim 4, wherein the functional relationship between the process factor, the edge light intensity shift, and the gradient of the optical image is changed for each pattern pitch. A program for predicting the size of a resist pattern formed by transferring a mask pattern to a resist on a wafer using a projection exposure apparatus,
A first procedure for setting a position where a dimension of the resist pattern is to be predicted and a desired dimension, and a second procedure for setting a relationship between a gradient of an optical image formed on the wafer, a process factor, and an edge light intensity shift. A third procedure for calculating and obtaining an optical image obtained by projecting the mask pattern onto the wafer by the projection exposure apparatus; and a first procedure based on the optical image obtained in the third procedure. A fourth procedure for obtaining a gradient of the optical image corresponding to a desired dimension at the dimension prediction position set in the step, and a process based on the relation set in the second procedure based on the gradient obtained in the fourth procedure. A fifth procedure for obtaining a factor and an edge light intensity shift; a sixth procedure for modulating the optical image according to the process factor and the edge light intensity shift obtained in the fifth procedure; procedure Computer readable recording medium a program stored for controlling the computer so as to execute a seventh step of extracting the dimension of the resist pattern from the optical image that has been subjected to modulation, the.

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