JPH11274028A - Method for proximity effect correction for electron beam drawing - Google Patents
Method for proximity effect correction for electron beam drawingInfo
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- JPH11274028A JPH11274028A JP7024598A JP7024598A JPH11274028A JP H11274028 A JPH11274028 A JP H11274028A JP 7024598 A JP7024598 A JP 7024598A JP 7024598 A JP7024598 A JP 7024598A JP H11274028 A JPH11274028 A JP H11274028A
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- proximity effect
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Abstract
Description
【0001】[0001]
【発明の属する技術分野】本発明は、試料上に微細なパ
ターンを描画するための電子ビーム描画技術に係わり、
特に近接効果の影響を低減するための電子ビーム描画に
おける近接効果補正方法に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electron beam writing technique for writing a fine pattern on a sample.
In particular, the present invention relates to a proximity effect correction method in electron beam writing for reducing the influence of the proximity effect.
【0002】[0002]
【従来の技術】電子ビーム描画装置によるパターン形成
は、光露光に比べて遙かに微細なパターン形成が可能で
あるために、今後のリソグラフィープロセスの主流とな
ろうとしている。ところで、電子ビームを用いた描画に
おいては、近接効果によるパターン寸法の精度の劣化が
問題となる。これは、以下の理由による。2. Description of the Related Art Pattern formation by an electron beam lithography apparatus is expected to become the mainstream of the lithography process in the future because it can form a pattern much finer than light exposure. By the way, in drawing using an electron beam, there is a problem that the accuracy of the pattern dimension is deteriorated due to the proximity effect. This is for the following reason.
【0003】いま、試料面上の位置x=(0,0)に広
がりの無視できる電子ビームが入射されたとする。入射
された電子の一部及び二次電子は、試料内で散乱されて
試料表面に戻り、これがレジストにエネルギーを与え
る。レジストに与えるエネルギー分布は、レジスト内で
の電子の散乱が無視できるならば、 δ(x)+ηρ(x) で与えられる。ここで、ηは散乱の程度を示すパラメー
タであり、ρ(x)は散乱電子の広がりを表す関数であ
る。Now, it is assumed that an electron beam having a negligible spread is incident on a position x = (0,0) on the sample surface. Some of the incident electrons and secondary electrons are scattered within the sample and return to the sample surface, which gives energy to the resist. The energy distribution given to the resist is given by δ (x) + ηρ (x) if electron scattering in the resist is negligible. Here, η is a parameter indicating the degree of scattering, and ρ (x) is a function indicating the spread of scattered electrons.
【0004】試料面上の電子の照射量分布をD(x)と
すると、散乱電子の影響を含めた実効的な照射量分布
は、 D(x)+η∫ρ(x−x’)D(x’)dx’ で与えられる。上式の第2項がいわゆる近接効果を示
す。近接効果を補正して正確なパターン寸法精度を得る
ためには、次のようにする。ここでは、成形ビームを用
いた描画を考える。照射した領域の縁では、ビームのぼ
けの効果を含めてレジストに与えられたエネルギー分布
は、与えられた量D0(x)に対して、 D(x)/2+η∫ρ(x−x’)D(x’)dx’=D0(x)…(1) で評価され、通常D(x)はD0(x)を定数d0とし
て、 D(x)/2+η∫ρ(x−x’)D(x’)dx’=d0 …(2) となるように定める。Assuming that the dose distribution of electrons on the sample surface is D (x), the effective dose distribution including the effect of scattered electrons is D (x) + η∫ρ (xx ′) D ( x ′) dx ′. The second term in the above equation indicates the so-called proximity effect. In order to correct the proximity effect and obtain accurate pattern dimensional accuracy, the following is performed. Here, drawing using a shaped beam is considered. At the edge of the illuminated area, the energy distribution imparted to the resist, including the effect of beam blur, is given by D (x) / 2 + η∫ρ (xx ′) for a given amount D0 (x). D (x ′) dx ′ = D0 (x) (1) where D (x) is usually D (x) / 2 + η∫ρ (xx ′) D, where D0 (x) is a constant d0. (X ′) dx ′ = d0 (2)
【0005】これに対してパブコビッチ(Pavkovich:J.
Vac.Schi.Techn.B4(1986)59 )は、上記(2)式の左辺
第2項をη∫ρ(x−x’)D(x)dx’で近似して Dp(x)=d0/{0.5+η∫ρ(x−x’)dx’} …(3) で与えた。しかしながら、この場合は上記の近似に伴う
誤差が生じる。これは、高い精度を求める場合には無視
できず、式(2)のより正確な解が必要となる。On the other hand, Pavkovich (J.
Vac.Schi.Techn.B4 (1986) 59) approximates the second term on the left side of the above equation (2) with η∫ρ (xx ′) D (x) dx ′ and obtains Dp (x) = d0 /{0.5+η∫ρ(xx′)dx ′} (3) However, in this case, an error occurs due to the above approximation. This cannot be ignored when high accuracy is required, and requires a more accurate solution of equation (2).
【0006】 式(2)を D(x)=2d0−2η∫ρ(x−x’)D(x’)dx’ …(4) と変形し、まず右辺のD(x’)にDp(x’)を代入
してより高次の近似解D2(x)を求め、次に右辺のD
(x’)にD2(x’)を代入してより高次の近似解D
3(x)を求める。以下、この手順を繰り返してより高
次の近似解を求める。Equation (2) is transformed into D (x) = 2d0−2η∫ρ (xx ′) D (x ′) dx ′ (4), and first, Dp ( x ') to obtain a higher-order approximate solution D2 (x).
Substituting D2 (x ') for (x'), higher order approximate solution D
3 (x) is obtained. Hereinafter, this procedure is repeated to obtain a higher-order approximate solution.
【0007】実際の計算では領域を有限の領域に分割
し、それぞれの領域ではD(x)は一定として、位置x
iにおけるD(x)の値Diである∫ρ(xi−x’)
D(x’)dx’をΣρ(xi−xj)djdxjに置
き換えて計算し、各領域でのD(x)の値を求める。こ
こで、dxjは領域jの面積を表す。In the actual calculation, the area is divided into finite areas, and D (x) is fixed in each area, and the position x
∫ρ (xi−x ′) which is the value Di of D (x) at i
D (x ′) dx ′ is calculated by replacing D (x ′) dx ′ with Σρ (xi−xj) djdxj, and the value of D (x) in each region is obtained. Here, dxj represents the area of the region j.
【0008】しかしながらこの方式では、一般に解の収
束速度が遅くて計算時間が長くなる上に、解が収束しな
いこともある。例えば、図4に示すような場合について
計算を行うと、解は収束しなかった。なお、図4では大
きなパターン41に隣接して小さなパターン42が配置
されている状態を示している。大パターン41の幅は9
8,小パターン42の幅は1、パターン間距離は1であ
る。また、ρ(x)=exp(−x2 )、η=0.3の
条件とした。However, in this system, the convergence speed of the solution is generally slow, the calculation time is long, and the solution may not converge. For example, when calculations were performed for the case shown in FIG. 4, the solution did not converge. FIG. 4 shows a state where a small pattern 42 is arranged adjacent to a large pattern 41. The width of the large pattern 41 is 9
8. The width of the small pattern 42 is 1, and the distance between the patterns is 1. Further, the conditions were set such that ρ (x) = exp (−x 2 ) and η = 0.3.
【0009】また、領域内の異なる位置x1,x2,…
におけるD(x)の値D(x1),D(x2),…に対
して、連立方程式を式(3)より導き直接D(x)を求
めることも原理的には可能であるが、これは膨大な計算
時間を必要とし実用的ではない。Also, different positions x1, x2,.
It is theoretically possible to directly derive a simultaneous equation from equation (3) for the value D (x1), D (x2),. Requires a lot of computation time and is not practical.
【0010】[0010]
【発明が解決しようとする課題】このように、従来の近
接効果補正方法においては、実用的には高い精度を得る
ことは困難であった。本発明は、上記事情に鑑みてなさ
れたものであり、その目的とするところは、従来よりも
高速で高精度に照射量分布を得ることができ、描画精度
の向上等に寄与し得る電子ビーム描画における近接効果
補正方法を提供することにある。As described above, in the conventional proximity effect correction method, it has been practically difficult to obtain high accuracy. The present invention has been made in view of the above circumstances, and an object of the present invention is to obtain an irradiation dose distribution at higher speed and higher accuracy than in the past, and to contribute to improvement of drawing accuracy and the like. An object of the present invention is to provide a proximity effect correction method in drawing.
【0011】[0011]
【課題を解決するための手段】(構成)上記課題を解決
するために本発明は、次のような構成を採用している。
即ち本発明は、電子ビーム描画における近接効果補正方
法において、試料面上xの位置にD(x)の照射量の電
子ビームを照射した時に、位置x’における近接効果の
影響がη∫ρ(x−x’)D(x’)dx’(η:定
数、ρ:関数、∫は試料面上の積分)と与えられる時、
与えられた量D0(x)に対して D(x)/2+η∫ρ(x−x’)D(x’)dx’=D0(x)…(1) となるようにD(x)を決めるために、D(x)を繰り
返し計算によって順次高次の近似項を求める時に、nを
正の実数としてn番目に求められる解Dn(x)に対し
てn+1番目に与えられる解Dn+1(x)を、例えばD0
(x)を定数d0として、 Dn+1(x)=(1−λ)Dn(x) +λ{2×d0−2×η∫ρ(x−x’)Dn(x’)dx’…(5) と与え、且つ0<λ<1に設定することを特徴とする。(Structure) In order to solve the above-mentioned problem, the present invention employs the following structure.
That is, according to the proximity effect correction method in electron beam writing, when the position of x on the sample surface is irradiated with an electron beam having a dose of D (x), the influence of the proximity effect at the position x ′ is η∫ρ ( xx ′) D (x ′) dx ′ (η: constant, ρ: function, ∫ is integral on the sample surface),
For a given quantity D0 (x), D (x) is set such that D (x) / 2 + η∫ρ (xx ′) D (x ′) dx ′ = D0 (x) (1) In order to decide, when finding higher order approximation terms sequentially by iteratively calculating D (x), the solution Dn + 1 given to the (n + 1) th solution Dn (x) with respect to the nth solution Dn (x) where n is a positive real number (x), for example, D0
Assuming that (x) is a constant d0, Dn + 1 (x) = (1−λ) Dn (x) + λ {2 × d0−2 × η∫ρ (xx ′) Dn (x ′) dx ′. 5) and 0 <λ <1.
【0012】ここで、本発明の望ましい実施態様として
は、次のものがあげられる。 (1) 前記の式(5)の近似解は、領域を分割して個々の
領域に対して与えられるものであり、高次の近似解を求
める際に既に高次の近似解が求められる領域があるとき
には、式(5)の右辺のDn(x’)の値を高次の近似
解の値を用いること。 (2) 前記の式(5)を用いて高次の近似解を求める時
に、領域を互いに少なくとも一部が他の領域に囲まれる
ように少なくとも2つの領域に分割し、順次各領域にお
いて近似解を求めること。 (3) 複数の演算手段を用いた並列演算を用いることによ
り、近似解を複数の点において同時に求めること。Here, preferred embodiments of the present invention include the following. (1) The approximate solution of the above equation (5) is given to individual regions by dividing the region, and when a higher-order approximate solution is obtained, a region where a higher-order approximate solution is already obtained If there is, use the value of a higher-order approximate solution for the value of Dn (x ') on the right side of equation (5). (2) When obtaining a higher-order approximate solution using the above equation (5), the region is divided into at least two regions so that at least a part of each region is surrounded by another region, and the approximate solution is sequentially determined in each region. To ask. (3) To obtain an approximate solution at a plurality of points at the same time by using a parallel calculation using a plurality of calculation means.
【0013】(作用)本発明によれば、上記の式(5)
において0<λ<1とすることで、近似計算の収束速度
を高め、また最新の近似データを用いて近似計算を行う
ことで更に収束速度を高めることができる。従って、高
速度で高精度に照射量を求めることができ、描画精度の
向上に寄与することが可能となる。(Operation) According to the present invention, the above equation (5)
By setting 0 <λ <1, the convergence speed of the approximate calculation can be increased, and the convergence speed can be further increased by performing the approximate calculation using the latest approximate data. Therefore, the irradiation amount can be obtained at high speed and with high accuracy, and it is possible to contribute to improvement in drawing accuracy.
【0014】[0014]
【発明の実施の形態】以下、本発明の詳細を図示の実施
形態によって説明する。なお、簡単のためにここでは、
D0(x)=d0とできる場合を説明する。図1は、本
発明の一実施形態に係わる近接効果補正方法を説明する
ためのフローチャートである。電子ビームを照射する小
領域の位置の座標は有限個x1,x2,…,xmとし、
その各々の場所の照射量をd1,d2,…,dmとする
(ステップS1)。補正計算は、以下のように行う。DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The details of the present invention will be described below with reference to the illustrated embodiments. Note that here, for simplicity,
A case where D0 (x) = d0 can be described. FIG. 1 is a flowchart for explaining a proximity effect correction method according to an embodiment of the present invention. The coordinates of the position of the small area to be irradiated with the electron beam are finite numbers x1, x2,.
.., Dm (step S1). The correction calculation is performed as follows.
【0015】まず、パブコビッチの解Dp(x)を求め
る。位置xi(i=1,2,…,m)における∫ρ
(x’−xi)D(x’)dx’は、具体的にはΣρ
(xi−xj)dxjと計算される(ステップS2)。
ここで、Σはj≠iなるjについての和、dxjはxj
を含む小領域の面積である。従って、xiにおける第一
近似解di1は di1=d0/(0.5+ηΣρ(xi−xj)dxj) …(6) で与えられる(ステップS3)。Σρ(xi−xj)d
xjを計算するときには計算を高速化するために、ρ
(xi−xj)が与えられた有限の値以上を持つ領域の
xjについてのみ計算する。通常は、ρ∝e exp(−x
2 / σ2 )となるとき、x〜50とすれば十分である。
さらに、代表図形法(Jpn.J.Appl.Phys.30(1991)2965)
を用いることもできる。First, a solution of Pavkovich Dp (x) is obtained. ∫ρ at position xi (i = 1, 2,..., M)
(X′−xi) D (x ′) dx ′ is, specifically, Σρ
It is calculated as (xi-xj) dxj (step S2).
Where Σ is the sum of jjj and dxj is xj
Is the area of the small region including. Therefore, the first approximate solution di1 at xi is given by di1 = d0 / (0.5 + ηΣρ (xi−xj) dxj) (6) (step S3). Σρ (xi-xj) d
When calculating xj, to speed up the calculation, ρ
Calculation is performed only on xj of the area where (xi-xj) has a given finite value or more. Usually, ρ∝e exp (−x
2 / σ 2 ), it is sufficient to set x to 50.
Furthermore, the representative figure method (Jpn.J.Appl.Phys.30 (1991) 2965)
Can also be used.
【0016】このdi1を第一近似として次に第二近似 di2=(1−λ)di1 +λ(2d0−2ηΣρ(xi−xj)dj1dxj) …(7) を求める(ステップS4)。Using this di1 as a first approximation, a second approximation di2 = (1−λ) di1 + λ (2d0−2ηΣρ (xi−xj) dj1dxj) (7) is obtained (step S4).
【0017】以下、上記の式(7)の右辺のdijの位
置にdj2を代入して第三近似di3が求められる。こ
の手順を繰り返して高次の近似解dik(k=2,3,
…)が求められる。この繰り返し計算は、例えば必要な
精度εに対して、dik/2+ηΣρ(xi−xj)d
j1dxjとd0との差をεiとするときに(ステップ
S5)、 (Σ|εi|dxi)/Σdxi < ε …(8) となるまで繰り返す(ステップS6)。ここで、Σは全
ての項についての和をとる。また、各領域dxiの大き
さは等しい必要はない。Hereinafter, the third approximation di3 is obtained by substituting dj2 for the position of dj on the right side of the above equation (7). By repeating this procedure, a higher-order approximate solution dik (k = 2, 3,
…) Is required. This iterative calculation is performed, for example, for a required accuracy ε, by dik / 2 + ηΣρ (xi−xj) d
When the difference between j1dxj and d0 is εi (step S5), the process is repeated until (Σ | εi | dxi) / Σdxi <ε (8) (step S6). Here, Σ takes the sum of all terms. Further, the sizes of the regions dxi need not be equal.
【0018】ここで、di(k+1)を求める際に行う
Σρ(xi−xj)djkdxjの計算においては、既
に領域jにおいて高次の近似解dj(k+1)が得られ
ているときにはdjkの代わりにdj(k+1)を用い
ることで収束性と収束速度を高くする。Here, in the calculation of Σρ (xi-xj) djkdxj performed when di (k + 1) is obtained, if a higher-order approximate solution dj (k + 1) has already been obtained in region j, djk is used instead of djk. By using dj (k + 1), convergence and convergence speed are increased.
【0019】また、dikをi=1,2,…と順に求め
るのではなくて、図2に示すように全領域をA,B二つ
の領域に分割して、先に領域Aに含まれる点に対して近
似解を求め次に領域Bに含まれる近似解を求めるように
する。領域の分け方は3つ以上にしてもよい。Further, instead of obtaining dik in order of i = 1, 2,..., The entire area is divided into two areas A and B as shown in FIG. , An approximate solution is obtained, and then an approximate solution included in the area B is obtained. The area may be divided into three or more.
【0020】図3は異なるλの値について、図4と同じ
条件で解を求めた時の解の収束の様子を示す。図3
(a)は式(7)で和をとるときに最新の値への置き換
えを行わない場合である。λ=1では解は発散する。λ
≦0.7で収束するが、λを小さくすると収束速度は遅
くなる。図3(b)は領域を2つに分けて計算する場合
で、この場合はλ>1を含む範囲で収束し0.7〜0.
9で収束速度が速い、λ<1において収束速度が速い。FIG. 3 shows the convergence of the solution when the solution is obtained under the same conditions as in FIG. 4 for different values of λ. FIG.
(A) is a case where replacement with the latest value is not performed when the sum is calculated in equation (7). At λ = 1, the solution diverges. λ
The convergence is achieved at ≦ 0.7, but the convergence speed decreases as λ decreases. FIG. 3B shows a case where the calculation is performed by dividing the region into two regions. In this case, the region converges in a range including λ> 1 and the range is 0.7 to 0.
9, the convergence speed is high, and when λ <1, the convergence speed is high.
【0021】このように本実施形態によれば、λを1よ
り小さく設定することにより、近似解の収束速度を速く
することができる。このため、高速で高精度に照射量分
布を求めることができ、近接効果の補正に極めて有効と
なる。さらに、(5) の演算を並列演算の可能な手段を用
いることによって多点で同時に行うことにより、計算速
度を速めることができる。As described above, according to the present embodiment, by setting λ to be smaller than 1, the convergence speed of the approximate solution can be increased. Therefore, the dose distribution can be obtained at high speed and with high accuracy, which is extremely effective for correcting the proximity effect. Furthermore, the calculation speed can be increased by simultaneously performing the calculation of (5) at multiple points by using means capable of parallel calculation.
【0022】なお、本発明は上述した実施形態に限定さ
れるものではない。実施形態では、ρ(x)としては単
純なガウス分布で与えられる場合について説明したが、
本発明は例えば複数のガウス分布の和の形で表される場
合にも適用できる。その他、本発明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。The present invention is not limited to the above embodiment. In the embodiment, the case where ρ (x) is given by a simple Gaussian distribution has been described.
The present invention can also be applied to a case where a plurality of Gaussian distributions are represented, for example. In addition, various modifications can be made without departing from the scope of the present invention.
【0023】[0023]
【発明の効果】以上詳述したように本発明によれば、前
記式(5)を用いて近似解を求める際に、0<λ<1と
設定することによって、高い精度の照射量分布を高速度
で計算できる。即ち、近似解の収束速度を高めることが
でき、描画精度の向上に寄与することが可能となる。As described above in detail, according to the present invention, when an approximate solution is obtained by using the above equation (5), by setting 0 <λ <1, a highly accurate dose distribution can be obtained. Can be calculated at high speed. That is, the convergence speed of the approximate solution can be increased, and it is possible to contribute to the improvement of the drawing accuracy.
【図1】本発明の一実施形態に係わる近接効果補正方法
を説明するためのフローチャート。FIG. 1 is a flowchart for explaining a proximity effect correction method according to an embodiment of the present invention.
【図2】同実施形態における領域分割の例を示す図。FIG. 2 is an exemplary view showing an example of area division in the embodiment.
【図3】同実施形態を用いた場合の解の収束の様子を示
す図。FIG. 3 is a view showing a state of convergence of a solution when the embodiment is used.
【図4】近接効果補正の計算条件の一例を示す図。FIG. 4 is a diagram showing an example of calculation conditions for proximity effect correction.
41…大パターン 42…小パターン S1〜S5…ステップ 41 large pattern 42 small pattern S1 to S5 step
Claims (1)
子ビームを照射した時に、位置x’における近接効果の
影響がη∫ρ(x−x’)D(x’)dx’(η:定
数、ρ:関数、∫は試料面上の積分)と与えられる時、
与えられた量D0(x)に対して D(x)/2+η∫ρ(x−x’)D(x’)dx’=
D0(x) となるようにD(x)を決めるために、D(x)を繰り
返し計算によって順次高次の近似項を求める時に、nを
正の実数としてn番目に求められる解Dn(x)に対し
てn+1番目に与えられる解Dn+1(x)を、 Dn+1(x)=(1−λ)Dn(x)+λ{2×D0
(x)−2×η∫ρ(x−x’)Dn(x’)dx’} と与え、且つ0<λ<1に設定することを特徴とする電
子ビーム描画における近接効果補正方法。When an electron beam having a dose of D (x) is applied to a position x on a sample surface, the effect of the proximity effect at the position x ′ is η∫ρ (xx ′) D (x ′). When given as dx ′ (η: constant, ρ: function, ∫ is integral on the sample surface),
For a given quantity D0 (x), D (x) / 2 + η∫ρ (xx ′) D (x ′) dx ′ =
In order to determine D (x) so as to obtain D0 (x), when successively obtaining higher-order approximation terms by repeatedly calculating D (x), an n-th solution Dn (x ), The solution Dn + 1 (x) given to the (n + 1) th is given by: Dn + 1 (x) = (1−λ) Dn (x) + λ {2 × D0
(X) −2 × η {ρ (xx ′) Dn (x ′) dx ′}, and 0 <λ <1.
Priority Applications (1)
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JP7024598A JPH11274028A (en) | 1998-03-19 | 1998-03-19 | Method for proximity effect correction for electron beam drawing |
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JP7024598A JPH11274028A (en) | 1998-03-19 | 1998-03-19 | Method for proximity effect correction for electron beam drawing |
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JPH11274028A true JPH11274028A (en) | 1999-10-08 |
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JP7024598A Pending JPH11274028A (en) | 1998-03-19 | 1998-03-19 | Method for proximity effect correction for electron beam drawing |
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JP (1) | JPH11274028A (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2013157623A (en) * | 2008-09-18 | 2013-08-15 | Nuflare Technology Inc | Drawing method and drawing device |
-
1998
- 1998-03-19 JP JP7024598A patent/JPH11274028A/en active Pending
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2013157623A (en) * | 2008-09-18 | 2013-08-15 | Nuflare Technology Inc | Drawing method and drawing device |
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