JP4189232B2 - Pattern forming method and drawing method - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a pattern forming method and a drawing method.
[0002]
[Prior art]
The pattern forming method using an electron beam can form a pattern much finer than that using light, and is used for trial manufacture of a semiconductor element. Moreover, in the pattern formation method using an electron beam, it is used also for producing the mask used for optical lithography.
[0003]
FIG. 1 shows an example of the configuration of a drawing apparatus using such an electron beam.
[0004]
The electron beam emitted from the electron gun 1 is focused by the focusing lens 2 and irradiated to the first shaping aperture 3. The image of the first shaping aperture 3 is formed on the second shaping aperture 5 by the projection lens 4.
[0005]
Here, a shaping deflector 6 is provided inside the projection lens 4, and the position of the image formed by the first shaping aperture is adjusted on the second shaping aperture 5 by the shaping polarizer 6. By doing so, a rectangular or triangular beam of any size is obtained.
[0006]
The image formed by the second shaping aperture 5 is reduced by the objective lens 7 and formed on a sample, for example, a reticle mask 8.
[0007]
The irradiation position of the beam on the reticle mask 8 is largely deflected to the center of the sub deflection region by the high-precision main deflector 9 and finely adjusted in the sub deflection region 11 by the high speed sub deflector 10.
[0008]
The reticle mask 8 alternately performs a stage-step movement that moves between the frames 12 and a continuous stage movement that moves continuously within the frame 12.
[0009]
In such an electron beam drawing apparatus, a pattern accuracy error called a proximity effect is seen. This proximity effect will be described below.
[0010]
As shown in FIG. 2, the incident electrons 14 incident on the sample 13 are scattered in the sample 13 to generate secondary electrons. A certain percentage of these secondary electrons and scattered incident electrons sensitize the resist 16 formed on the surface of the sample 13 as backscattered electrons 15. That is, the background irradiation amount is generated in addition to the irradiation amount by the incident electrons. The spread of the photosensitivity is, for example, about 10 μm in radius with a 50 keV apparatus.
[0011]
Further, the exposure amount of the resist by the backscattered electrons 15 varies depending on the density of the pattern to be formed. Since the pattern size after resist development is determined by exposure that combines exposure by original incident electrons 14 and exposure by backscattered electrons 15, the pattern size after development varies depending on the density of the pattern.
[0012]
This is called a proximity effect. Proximity effects may also be caused by beam blur, electron scattering in the resist, or the like.
[0013]
Further, in the electron beam drawing apparatus, a pattern accuracy error called a long-distance photosensitive action is also seen. Hereinafter, this long-distance photosensitive action will be described.
[0014]
As shown in FIG. 3, it is assumed that incident electrons 14 are incident on the surface of the sample 13. Part of the incident electrons 14 and secondary electrons are emitted from the sample surface and return to the lower surface 18 of the objective lens 17 of the apparatus. The re-reflected electrons 19 further reflected by the lower surface 18 return to the resist 16 to be exposed. That is, a background irradiation amount is generated.
[0015]
This phenomenon is called long-distance photosensitivity. The range of this long-distance photosensitive action extends over an area of several tens of millimeters from the beam irradiation position. Therefore, when there is a large distribution in the average irradiation amount on the scale of the sample on the scale of several millimeters, the resist pattern dimensions after development Produces a large size distribution.
[0016]
On the other hand, when the pattern is formed by etching the sample using the resist pattern as a mask, the pattern size varies because the etching progresses mainly depending on the pattern density. This is called a loading effect.
[0017]
The dimensional variation due to this loading effect largely depends on the pattern density of the formed resist pattern. The microloading effect is corrected after the proximity effect is corrected (see, for example, Patent Document 1).
[0018]
[Patent Document 1]
Japanese Patent No. 3074675
[0019]
[Problems to be solved by the invention]
In the conventional pattern forming method including energy beam drawing, there is a problem that pattern dimension variation occurs due to a loading effect during etching. In Patent Document 1, the microloading effect is corrected after the proximity effect is corrected. However, an irradiation amount for correcting the microloading effect is experimentally obtained. However, as will be described later, since the loading effect interacts with the proximity effect and the long-distance photosensitive action, accurate correction cannot be performed simply by determining the correction dose for correcting the loading effect.
The present invention has been made in view of such problems, and it is an object of the present invention to provide a pattern forming method and a drawing method in which a highly accurate correction dose is determined and the resulting dimensional variation is constant regardless of the pattern density. And
[0020]
[Means for Solving the Problems]
A pattern drawing method according to a first aspect of the present invention is a pattern drawing method for drawing a pattern by irradiating a sample coated with a resist with an energy beam, wherein the drawing data for drawing the pattern, the energy beam Reference dose D for irradiating₀, Storing the pattern dependence distribution of the dimensional variation Δ due to the influence of the loading effect, and the energy distribution s given to the resist of the energy beam, and dividing the drawing area into a lattice shape to form a sub-drawing area A step of obtaining a pattern area density distribution for each of the sub-drawing regions based on the drawing data, the pattern area density and the reference dose D₀The dose DC for correcting the long-distance photosensitive action in the sub-drawing area based on_fThe step of calculating (x), the drawing data and the reference dose D₀The dose DC for correcting the proximity effect for the pattern in the sub-drawing area based on_pA step of calculating (x) and a dose DC for correcting the long-distance photosensitivity._f(X) Dose DC for correcting the proximity effect_p(X), a step of obtaining a dose D (x) based on the pattern dependence distribution of the dimensional variation Δ and the energy distribution s of the energy beam, and data on the position and shape of the pattern in the sub-drawing region And determining the irradiation position and shape of the energy beam based on the above and irradiating the energy beam for a time period corresponding to the irradiation amount D (x).
[0021]
A step of obtaining a dimensional variation distribution Δ (x) in each of the sub-drawing regions from the pattern area density distribution and a pattern-dependent distribution of the dimensional variation Δ due to the loading effect. Dose DC to correct long-range photosensitivity_f(X) is the pattern area density distribution and the reference dose D.₀, And a dose DC that is calculated based on the dimension variation distribution Δ (x) and corrects the proximity effect_p(X) is data relating to the position and shape of the pattern in the sub-drawing region, and the reference dose D₀The calculation may be performed based on the dimension variation distribution Δ (x) and the energy distribution s of the energy beam.
The dose D (x) is a dose DC for correcting the proximity effect._p(X) and dose DC for correcting the long-distance photosensitivity_fYou may comprise so that it may be a product with (x).
Note that the dose DC for correcting the long-distance photosensitive action_f(X) is the reference dose D.₀The dose D (x) may be calculated as follows.
The dose D (x) is D (x) = DC._p(X) x DC_f(X) / (1+ (2s (Δ) −1) × (DC_p(X) x DC_f(X) / D₀)).
The dimensional variation Δ may include a dimensional variation due to the influence of non-uniformity in the etching rate of the resist in addition to the loading effect.
Note that the dose DC for correcting the long-distance photosensitive action_f(X) is the reference dose D.₀The dose D (x) may be determined as
[0022]
According to a second aspect of the present invention, there is provided a pattern forming method comprising: a step of drawing a pattern on the resist using the pattern drawing method; and developing the resist to form a resist pattern; and masking the resist pattern And etching the sample to form a pattern on the sample.
[0023]
Here, the loading effect refers to an effect in which, in the case of forming a pattern by etching a sample using a resist pattern as a mask, the etching progresses mainly depending on the pattern density.
[0024]
DETAILED DESCRIPTION OF THE INVENTION
Before describing the embodiment of the present invention, the inventors' discussion on the exposure amount of the electron beam in consideration of the loading effect will be described.
[0025]
FIG. 4 is a diagram showing the energy distribution given to the resist by the electron beam spot at the pattern edge in the case of drawing with the electron beam drawing apparatus.
[0026]
In FIG. 4, for simplicity, the energy distribution at the pattern edge is linear. Here, the sparse pattern region A and the dense pattern region B are corrected within a range where the influence of the proximity effect is considered without considering the loading effect. It is assumed that the two patterns are located at positions where the influence of the long-distance photosensitive action is almost equal.
[0027]
The irradiation amount of the sparse pattern region A is Dr, and the background irradiation amount due to the long-distance photosensitive action is DB_f, Df is the irradiation amount of the dense pattern region B, DB is the background irradiation amount due to the proximity effect_pAnd Since it is assumed that the sparse pattern area A and the dense pattern area B are located at positions where the influence of the long-distance photosensitive action is almost equal, the background irradiation amount due to the long-distance photosensitive action of the dense pattern area B is sparse. DB as in pattern area A_fIt becomes. Further, for the sake of simplicity in this example, it is assumed that the influence of the proximity effect can be ignored in the sparse pattern region A. In FIG. 4, w represents a half value of the spread at the pattern end face of the energy distribution given to the resist by incident electrons, which is about half the blur of the electron beam spot, ie, the center of the spread, Reference dose D₀The half of the position is the pattern edge of the resist pattern.
[0028]
The dose Dr of the sparse pattern region A and the dose Df of the dense pattern region B are respectively
0.5Dr + DB_f= 0.5D₀
0.5Df + DB_p+ DB_f= 0.5D₀
To satisfy the equation shown in. Here, background dose DB by proximity effect_pAnd background irradiation DB by long-distance photosensitive action_fRespectively, using the integral over the entire mask
DB_p= Η∫σ (xx ′) D (x ′) dx ′
DB_f= Θ∫p (xx ′) D (x ′) dx ′
Given in. Here, D (x) represents the dose of incident electrons at the position x, and η and θ are parameters indicating the effects of the proximity effect and the long-distance photosensitive action, respectively. Further, the integrand σ (x) represents the spread of the proximity effect. The integrand p (x) represents the spread of the long-distance photosensitive action.
[0029]
Here, since it is assumed that the influence of the loading effect is almost equal in the sparse pattern area A and the dense pattern area B, the dose DC for correcting the influence on the same loading effect in the two patterns._aAdd
[0030]
As shown in FIG. 5, a correction dose DC for correcting the influence on the loading effect is now applied to the sparse pattern region A._aSuppose that the size of the pattern can be corrected by Δ. That is, the corrected dose DC_aIs added to the reference dose D in the sparse pattern area A.₀The position where it becomes equal to half of the value is the corrected dose DC_aDose in the sparse pattern area A before adding the reference dose D₀It is made to move by Δ to the right in the drawing from a position equal to half of the value.
To do this,
(Dr + DC_a) (W−Δ) / 2w + (1 + DC)_a/ DC_mfDB_f= 0.5D₀
Corrected dose DC to satisfy_aYou can decide. DC_mfIs the background dose DB for long-distance photosensitivity_fIs the average dose in the integration region.
[0031]
Next, the corrected dose DC for correcting the influence on the loading effect in the dense pattern region B_aIf the change in the dimension of the pattern by adding
(Df + DC_a) (W−Δ ′) / 2w + (1 + DC)_a/ Df) DB_p+ (1 + DC_a/ DC_mfDB_f= 0.5D₀
It becomes. At this time,
DBar = (DC_a/ DC_mfDB_f,
DBaf = (DC_a/ Df) DB_p+ (DC_a/ DC_mfDB_f
Then,
As shown in FIG. 5, DBar and DBaf represent the increment of the background irradiation amount, and the dimensional variation Δ ′ in the dense pattern region B is larger than that in the sparse pattern region A.
[0032]
Now DB_p= Df / 3, background irradiation DB by long-distance photosensitive action_fAnd Δ ′ to 3Δ when calculating that Δ is very small compared to w. That is, the dimensional variation Δ ′ of the dense pattern region B is about three times the dimensional variation Δ of the sparse pattern region A.
[0033]
From the above, it can be seen that accurate correction cannot be performed simply by determining a uniform correction dose for correcting the loading effect.
Hereinafter, embodiments of the present invention will be described with reference to the drawings. The present invention is not limited to the following embodiments, and can be used with various modifications.
[0034]
FIG. 6 shows a glass mask having a side of 150 mm, and a case where drawing is performed on the glass mask by an electron beam drawing apparatus is considered.
[0035]
First, as shown in FIG._x, Δ_y(Δ_x~ Δ_y˜1 mm) square lattice (sub-drawing area). Where δ_x, Δ_yMay be a fraction of the typical size variation (about 10 mm) due to the long-distance photosensitive action.
[0036]
Further, in the electron beam drawing apparatus, when the size of the grating is larger than the size of the deflection region, it is preferable to increase the drawing efficiency by making the size of the grating an integral multiple of the size of the deflection region. For example, when the size of the deflection region is 500 μm square, the size of the grating is 1000 μm = 1 mm square. If the drawing area of a glass mask having a side of 150 mm is a 130 mm square, the size of the grid is 1 mm square, so the number of grids is 130 × 130 = 16900. The description will be made assuming that the deflection area is 1 mm square.
[0037]
First, the irradiation dose D (x) in each shot that combines the proximity effect, the long-distance photosensitivity action, and the loading effect correction is calculated.
0.5D (x) (w−Δ (x)) / w + η ＋ σ (xx ′) D (x ′) dx ′ + θ∫p (xx ′) D (x ′) dx ′ = 0. 5D₀(1)
Decide to meet. Each of x and x ′ represents a two-dimensional vector for convenience of description.
[0038]
Here, η and θ are parameters indicating the effects of the proximity effect and the long-distance photosensitive action, respectively. Also, σ (x) and p (x) are functions giving the spread of the proximity effect and the long-distance photosensitive action, respectively. These are obtained experimentally beforehand.
[0039]
Δ (x) gives a dimensional variation due to the loading effect at position x. It is considered as being constant within an area of about 1 mm square. Usually, the spread σ (x) of the proximity effect is about 10 μm, and the spread p (x) of the long-distance photosensitive action is about several mm.
[0040]
Here, in Equation (1), the integration range on the left side is the pattern area of the entire mask. However, practically, the integration range in the first integration including σ (xx ′) is limited to a region having a radius of about several tens of μm centered on the point x and includes p (xx ′). The integration range in the second integration may be limited to a region having a radius of about 30 mm centered on the point x.
[0041]
As a method for correcting the proximity effect and the long-distance photosensitive action, for example, the following method can be considered.
[0042]
D (x) = DC_p(X) x DC_f(X) As a dose DC to correct the long-distance photosensitivity_fDose DC whose change in (x) corrects the proximity effect_pIf it is more gradual than the change in (x), equation (1) is a good approximation.
0.5DC_p(X) DC_f(X) (w−Δ (x)) / w + ηDC_f(X) ∫σ (xx ′) DC_p(X ′) dx ′ + θ∫p (xx ′) DC_p(X ′) DC_f(X ′) dx ′ = 0.5D₀... (2)
It can be expressed as.
[0043]
Now, dose DC to correct proximity effect_p(X)
0.5DC_p(X) + ηw / (w−Δ (x)) ∫σ (xx ′) DC_p(X ′) dx ′ = 0.5 (3)
Decide to meet. Under this condition, the remaining equation is
0.5DC_f(X) + θw / (w−Δ (x)) （p (xx ′) DC_p(X ′) DC_f(X ′) dx ′ = 0.5 w / (w−Δ (x)) D₀... (4)
It becomes. The integration included in this equation (4) is a dose DC for correcting the long-distance photosensitivity in the area where the integration is performed with a size of about 1 mm square._fEven if (x) is determined to be constant, there is no significant error. When limited to this 1 mm square region, the term including the integral of equation (4) is
θw / (w−Δ (x)) × Σp (xx_jDC_f(X_j) ∫_jDC_p(X ′) dx ′
It becomes. Here, j is a subscript indicating the area, and ∫_jMeans integration in region j. The term including the integral of equation (4) is represented by the sum of the terms including the integral for each region.
[0044]
When integrating both sides of equation (3) in the region where the pattern of the region j of about 1 mm square exists, the integration of the second term on the left side is a double two-dimensional space integration.
∫_j∫σ (xx ′) DC_p(X ′) dx′dx
It becomes.
Where ∫_jConsider the part of σ (x−x ′) dx. The value of integration varies depending on how much the pattern exists in the region centered on the position x '. However, if the pattern is dense, if x ′ is included in the region j, it may be approximated as 1 regardless of x ′. Therefore, this value is 1 as the first approximation. In this case, the above integral is
DC_p(X) was integrated in the 1 mm square region j.
∫_jDC_p(X ′) dx ′
It becomes. After all
(0.5 + ηw / (w−Δ (x_i))) ∫_jDC_p(X ′) dx ′ = 0.5 × (pattern area in region j)
Is obtained. That means
∫_jDC_p(X ′) dx ′ = 0.5 × (pattern area in region j) / (0.5 + ηw / (w−Δ (x_i))
And equation (4) is for region i
0.5DC_f(X_i) + Θw / (w−Δ (x_i)) / (0.5 + ηw / (w−Δ (x))) Σp (x_i-X_jDC_f(X_j) × 0.5 × (pattern area in region j) = 0.5 w / (w−Δ (x_i)) D₀(5)
It becomes. This equation (5) is applied to each area of the entire mask to make DC_f(X_i).
In order to further improve the accuracy of approximation, the pattern density e in this region j_jE_j= (Pattern area in region j) / (area of region j) and ∫σ (x−x ′) dx is defined as e_jAnd can be approximated. At this time
(0.5 + e_jηw / (w−Δ (x_i))) ∫DC_p(X ′) dx ′ = 0.5 × (pattern area in region j)
So equation (4) is slightly different from (5)
0.5DC_f(X_i) + Θw / (w−Δ (x_i)) Σ1 / (0.5 + e_jηw / (w−Δ (x_i))) P (x_i-X_jDC_f(X_j) × 0.5 × (pattern area in region j) = 0.5 w / (w−Δ (x_i)) D₀.... (5 ')
It becomes.
It is also possible to obtain DCp (x) directly from (3) strictly or using an appropriate approximation and substitute it in (4) to increase the calculation accuracy.
[0045]
Since the size of the mask is larger than the spread of p (x), x in Σ in equation (5)_iIf only the area within a radius of 30 mm, for example, is calculated from the area including, the calculation becomes easier.
[0046]
In the method described in equations (5) and (5 '), DC_f(X_i) Indicates the parameter η indicating the effect of the proximity effect, the parameter θ indicating the effect of the long-distance photosensitive action, and the fine pattern distribution required when performing the proximity effect correction if the pattern area in each region is known. Is not necessary.
[0047]
Dose DC to correct long-range photosensitivity_f(X) is obtained in advance, and at the time of drawing, a dose DC for correcting the proximity effect obtained by calculating the vicinity of the drawing region_pDose DC for calculating (x) and correcting the proximity effect given to the region_fBy multiplying the value of (x), it is possible to correct all of the proximity effect, the long-distance photosensitive action, and the loading effect.
[0048]
The pattern density dependence of the dimensional variation Δ caused by the loading effect can be obtained by etching resist patterns having different pattern densities.
[0049]
Here, the simplest linear distribution is assumed as the effective dose distribution, but other distribution may be used as a matter of course. Let u be the dimensional variation Δ due to the loading effect, and u = 0 at the pattern edge, now considered one-dimensionally. Further, it is assumed that the dose distribution is given by D (x) × s (u). However, s (u) represents the energy distribution given to the resist by the beam spot, and s (0) = 0.5, s (∞) = 0, and s (−∞) = 1.
[0050]
In the previous example (in the case of linear distribution), s (u) = 0.5 × (w−u) / w when −w ≦ u ≦ w, s (u) = 1 and u> w when u <−w. S (u) = 0.
[0051]
When the above-described method is used, the equation (1) for giving the dose D (x) is as follows.
[0052]
D (x) s (Δ) + η∫σ (xx ′) D (x ′) dx ′ + θ∫p (xx ′) D (x ′) dx ′ = 0.5D₀.... (6)
Here, as before, D (x) = DC_p(X) x DC_f(X)
DC_p(X) + η (1 / s (Δ)) ∫σ (xx ′) DC_p(X ′) dx ′ = 0.5 (7)
0.5DC_f(X) + θ (1 / s (Δ)) ∫p (xx ′) DC_p(X ′) DC_f(X ′) dx ′ = 0.5 (1 / s (Δ)) D₀... (8)
Dose DC to correct the proximity effect by solving_p(X) Dose DC for correcting long-range photosensitivity_f(X) can be obtained.
[0053]
The energy distribution s (Δ) given to the resist by the spot beam can be experimentally obtained from the dose dependency of the resist pattern dimension variation. For example, assuming an appropriate function form such as an error function, parameters may be determined by drawing a test pattern.
[0054]
A rectangular pattern is arranged in an array at an equal pitch, and an area that is sufficiently larger than the distance affected by the proximity effect and smaller than the distance affected by the loading effect, for example, an area having a size of 200 microns square, is arranged at the center. take. In this central part, linear patterns having different densities are drawn in an area of about 100 microns. Here, in the drawing of the central pattern, proximity effect correction and long-range photosensitive action correction are performed. A representative value of the dimensional variation in the pattern after development is defined as a dimensional variation Δ due to the influence of the loading effect on the peripheral pattern density. As the representative value, for example, it is desirable to use a dimensional variation Δ averaged around the most important density of the central pattern.
[0055]
FIG. 8 shows an example of a system configuration for realizing the above correction.
[0056]
First, the storage unit 20 of the system stores in advance a table of a function s (x) representing the dependency of the pattern area density on the size variation Δ due to the loading effect and the energy distribution of the spot beam.
[0057]
Next, drawing data and reference dose D₀Is input and stored in the storage means 21 of the data processing computer of the apparatus.
[0058]
Next, based on the drawing data stored in the storage unit 21, the calculation unit 24 divides the entire drawing region into 1 mm square lattices, and obtains the pattern area density for each 1 mm square lattice (sub drawing region).
[0059]
Next, from the pattern area density distribution and a table of the dependence of the pattern area density on the dimensional variation Δ due to the effect of the loading effect stored in the storage unit 20, the dimensional variation distribution of the dimensional variation Δ in the computing unit 25. Δ (x) is obtained, and a table of this dimensional variation distribution Δ (x) is stored in the storage means 26.
[0060]
Next, the pattern area density, the dimension variation distribution Δ (x) of the dimension variation Δ due to the influence of the loading effect, and the reference irradiation amount D₀From the above, the long-distance photosensitivity correction computer 27 solves the equation (8) to correct the long-distance photosensitivity DC._f(X) is obtained and the table is stored in the storage means 28.
[0061]
On the other hand, in the drawing system 22, at the time of drawing, the data processing computer extracts the pattern data in the sub drawing area from all the pattern data stored in the storage unit 21 and sends it to the figure dividing circuit 23.
[0062]
Next, the graphic dividing circuit 23 sends data relating to the position and shape of the small graphic in the sub drawing area obtained by the division to the proximity effect correction calculating circuit 29.
[0063]
At this time, the proximity effect correction calculation circuit 29 sends the position information of the sub drawing area to the storage means 26 in which the dimension fluctuation distribution Δ (x) due to the influence of the loading effect is stored, and the dimension fluctuation distribution corresponding to the sub drawing area. The value of Δ (x) is taken out.
[0064]
Further, the proximity effect correction calculation circuit 29 sends the value of this dimensional variation distribution Δ (x) to the storage means storing the function s representing the energy distribution given to the resist by the energy beam, and corresponding s (Δ ( x)) value is taken out.
[0065]
Next, based on the equation (7), the dose DC based on the proximity effect correction for each small figure in the sub drawing area_p(X) is calculated and output to the arithmetic circuit 30.
[0066]
Next, the arithmetic circuit 30 has a long distance photosensitive action correction dose DC stored in the storage means 28._fFrom the table of (x), the long-distance photosensitive action correction dose DC corresponding to the sub-drawing area_fThe value of (x) is taken out and the final corrected dose D (x) = DC_p(X) x DC_f(X) is obtained and output to the drawing circuit 31 together with data relating to the position and shape of each small figure.
[0067]
The drawing circuit 31 determines the irradiation position and shape of the electron beam based on the position and shape data of the small figure in the sub drawing area, and irradiates the sample with the electron beam for the irradiation time corresponding to the irradiation amount D (x). This is repeated until drawing is completed for all small figures in the sub drawing area. When the drawing in one sub drawing area is completed, the drawing moves to the next sub drawing area.
[0068]
Here, depending on the system and required conditions, the long-distance photosensitive action may be ignored. In that case, in the above process, the dose DC for correcting the long-distance photosensitive action_fThe step of obtaining (x) is omitted, and D (x) = DC_p(X) × D₀What should I do?
[0069]
In the above method, the parameter indicating the proximity effect in the proximity effect correction calculation is not η but ηw / (w−Δ (x)), and takes a different value for each lattice. However, considering the speeding up of the operation or the configuration of the correction operation circuit, the system configuration can be made easier if the parameter in the proximity effect correction is constant over the entire mask as η. Therefore, it is possible to do the following.
[0070]
First, without considering the loading effect, the irradiation effect D (x) in each shot is calculated by combining the proximity effect and the long-distance photosensitivity correction.
0.5D (x) + η∫σ (xx ′) D (x ′) dx ′ + θ∫p (xx ′) D_d(X ′) dx ′ = 0.5D₀(9)
Decide to meet. The description of x and x ′ indicates a two-dimensional vector for convenience. Here, η and θ are parameters indicating the effects of the proximity effect and the long-distance photosensitivity, respectively, and σ (x) and p (x) are functions that give the spread of the proximity effect and the long-distance photosensitivity, respectively. These are obtained experimentally beforehand.
[0071]
Usually, the spread σ (x) of the proximity effect is about 10 μm, and the spread p (x) of the long-distance photosensitive action is about several mm.
[0072]
For example, the following method can be considered as a method for correcting the proximity effect and the long-distance photosensitive action. D (x) = DC_p(X) x DC_f(X) As a dose DC to correct the long-distance photosensitivity_fDose DC whose change in (x) corrects the proximity effect_pAssuming that it is gradual compared to the change in (x), the above equation is a good approximation.
0.5DC_p(X) DC_f(X) + ηDC_f(X) ∫σ (xx ′) DC_p(X ′) dx ′ + θ∫p (xx ′) DC_p(X ′) DC_f(X ′) dx ′ = 0.5D₀... (10)
And can.
[0073]
Now, dose DC to correct proximity effect_p(X) and dose DC for correcting long-distance photosensitivity_f(X)
0.5DC_p(X) + η∫σ (xx ′) DC_p(X ′) dx ′ = 0.5 (11)
0.5DC_f(X) + θ∫p (xx ′) DC_p(X ′) DC_f(X ′) dx ′ = 0.5D₀(12)
Decide to meet. The integral included in equation (12) is about 1 mm square and the DC_fEven if (x) is determined to be constant, there is no significant error.
[0074]
When limited to this 1 mm square region, the term including the integral of equation (12) is
θΣp (xx_jDC_f(X_j) ∫_jDC_p(X ′) dx ′
It becomes. Here, j is a subscript indicating the area, and ∫_jMeans the integration in the region j, and the term including the integration of the equation (12) is represented by the sum of the terms including the integration for each region.
[0075]
When both sides of equation (11) are integrated in the area where the pattern of the area of about 1 mm square exists, the integration of the second term is a double two-dimensional space integration.
∫_j∫σ (xx ′) DC_p(X ′) dx′dx
It becomes. This is approximated as before
∫_jDC_p(X ′) dx ′
It becomes. If the integration area at x 'is this 1mm square area,
(0.5 + η) ∫_jDC_p(X ′) dx ′ = 0.5 × (pattern area of region j)
Is obtained. That means
∫_jDC_p(X ′) dx ′ = (pattern area of region j) / (0.5 + η)
Equation (12) is for region i
0.5DC_f(X_i) + Θ / (0.5 + η) Σp (x_i-X_jDC_f(X_j) × (pattern area of region j) = 0.5D₀(13)
It becomes. This equation (13) is simultaneously applied to each area of the entire mask so that DC_f(X_i).
[0076]
Since the size of the mask is larger than the spread of q (x), x in equation (13) is_iIf only the area within a radius of 30 mm, for example, is calculated from the area including, the calculation becomes easier.
[0077]
In the method described here, DC_f(X_i) Does not require the fine pattern distribution required when proximity effect correction is performed if θ, η, and the pattern area in each region are known.
[0078]
Dose DC to correct long-range photosensitivity_f(X) is obtained in advance, and the dose DC for correcting the proximity effect obtained by calculating the vicinity of the sub-drawing region at the time of drawing_pA dose DC that calculates (x) and corrects the long-range photosensitive action given to the sub-drawing area_fBy multiplying the value of (x), both the proximity effect and the long-distance photosensitive action can be corrected.
[0079]
Next, a corrected irradiation dose for the loading effect is obtained. Here, it is approximated that the dimensional variation does not depend on the pattern shape depending on the pattern density. In order to simplify the system, it is effective to use the same grid as the pattern density distribution used when correcting the long-distance photosensitive action.
[0080]
In the example of FIG. 4, it is assumed that the dimensions vary by Δ. In order to correct this dimensional variation, the dose is corrected as shown in FIG.
[0081]
In the example of the dense pattern region B in FIG. 4, the irradiation amount before the loading effect correction is D (x), and the effective background irradiation amount due to the proximity effect and the long-distance photosensitive action at this time is Db. Assuming that the corrected dose is Da (x), the background dose is
Db × Da (x) / D (x)
And approximate. here,
Db = 0.5 (D₀-D (x)) (15)
Given in. Therefore,
Da (x) × (w−Δ) / 2w + Db × Da (x) / D (x) = 0.5D₀... (16)
If Da (x) is selected so that, the resist size after development changes by -Δ. Since the dimensional variation due to etching is Δ, the two dimensional variations are canceled out to obtain a desired size after etching.
0.5D (x) + Db (x) = 0.5D₀
So solve equation (16)
Da (x) = D (x) / (1− (Δ / w) × D (x) / D₀(17)
Is obtained. By drawing with the irradiation amount Da (x), a desired dimension can be obtained after the etching process.
[0082]
The pattern density dependency of Δ can be obtained by etching resist patterns having different pattern densities.
[0083]
In the example of FIG. 7, the simplest linear distribution is assumed as the effective dose distribution, but other distributions may be used as a matter of course. Considering one dimension now, the position of the pattern edge is set to u = 0. Assume that the dose distribution is D (x) s (u). However, s (0) = 0.5, s (∞) = 0, and s (−∞) = 1. When the above-described method is used, it is as follows.
[0084]
(Da (x) / D (x)) × Db (x) + Da (x) s (Δ) = 0.5D₀  ... (18)
So,
Da (x) = D (x) / (1+ (2s (Δ) −1) × (D (x) / D₀)) (19)
What should I do? The energy distribution s (Δ) given to the resist by the spot beam can be experimentally determined from the dose dependency of the resist pattern dimension variation. For example, assuming an appropriate function form such as an error function, parameters may be determined by drawing a test pattern.
[0085]
An area in which rectangular patterns are arranged in an array at an equal pitch, and an area that is sufficiently larger than the distance affected by the proximity effect at the center and smaller than the distance affected by the loading effect, for example, an area having a size of 200 microns square I take the. In this central part, linear patterns having different densities are drawn in an area of about 100 microns. Here, in the drawing of the central pattern, proximity effect correction and long-range photosensitive action correction are performed. A representative value of the dimensional variation of the pattern after development is defined as a dimensional variation Δ due to variation of the loading effect on the peripheral pattern density. As the representative value, for example, it is desirable to use a dimensional variation Δ averaged around the most important density of the central pattern.
[0086]
The correction method described so far can be realized, for example, by adopting a system configuration as shown in FIG.
[0087]
First, the pattern density dependency of the dimensional variation Δ due to the variation of the loading effect and the function s (x) representing the energy beam distribution are obtained by experiment or simulation, and the table is stored in the storage means 20.
[0088]
Next, drawing data and reference dose D₀Is input and stored in the storage means 21 of the data processing computer of the apparatus.
[0089]
Next, the drawing data stored in the storage unit 21 is input to the calculation unit 24, and based on this, the entire area is divided into 1 mm square sub drawing areas, and the pattern area density of each sub drawing area is obtained.
[0090]
Next, the calculation means 32 solves the equation (13) on the basis of the pattern area density of each sub-drawing region, thereby determining the reference dose D₀The dose DC for correcting the long-distance photosensitive action of each sub-drawing area when_fA table (x) is created and stored in the storage means 33.
[0091]
On the other hand, the drawing system 22 inputs drawing data from the storage means 21 to the figure dividing circuit 23 at the start of drawing and cuts out each drawing figure.
[0092]
Next, using the proximity effect correction circuit 34, the reference dose is set to D based on the drawing data near the sub drawing area.₀Dose amount DC for proximity effect correction when_p(X) is determined using equation (11).
[0093]
Next, the loading effect correction circuit 35 corrects the long-distance photosensitive action corresponding to the sub-drawing area._fThe value of (x) is taken out from the storage means 33,
D (x) = DC_p(X) x DC_f(X)
Next, the dimensional variation Δ due to the loading effect corresponding to the pattern density is taken out from the storage means 20. Thereafter, the energy distribution s (Δ) relating to the spot beam is obtained from a table of the function s (x) representing the distribution of the energy beam stored in the storage means. Finally, Da (x) = D (x) / (1+ (2s (Δ) −1) × (D (x) / D₀)) And the irradiation amount Da (x) is sent to the drawing circuit 31.
[0094]
The drawing circuit 31 draws the sub drawing area with the given dose Da (x). The above process is repeated for all sub-drawing areas, and all the drawing areas are drawn. Since the values in the table are discrete, it is effective to use interpolation when obtaining the dimensional variation Δ due to the loading effect and the energy distribution s (Δ) related to the spot beam based on the table.
[0095]
Also, the dose DC for correcting the long-distance photosensitivity in advance._fIf the pattern density is calculated by obtaining drawing data slightly ahead of the current drawing during drawing instead of obtaining the table of (x), the pattern density calculation is performed almost in parallel with the drawing. Therefore, the dose DC for correcting the long-distance photosensitive action_fIt is possible to remove the calculation time required to create the table of (x).
[0096]
So far, it has been limited to correcting the loading effect. However, this method is also effective for correcting dimensional variations other than the loading effect.
[0097]
In an etching apparatus, it is ideal that the etching rate is uniform on the sample surface, but in reality, there is a slight distribution. If the dimensional variation of the pattern due to this non-uniformity of etching is given by the dimensional variation Δ regardless of the density of the pattern, it is possible to correct the dimension by using the correction equation (10) discussed above. is there.
[0098]
For this purpose, pattern dimension variation distribution data is used in advance and stored in the storage means in the form of a table or a mathematical expression obtained by fitting, and the energy distribution s (Δ) given to the resist by the spot beam is calculated. In this case, the correction amount is calculated by obtaining the dimensional variation Δ.
[0099]
Further, when both the loading effect and the etching non-uniformity exist, as shown in FIG. 10, the influence of both is obtained in advance, and the distribution ΔL of the dimensional variation due to the loading and the dimension due to the non-uniformity. A desired dimension can be obtained by applying the correction equation (10) to Δ as the sum ΔL + ΔU with the variation distribution ΔU.
[0100]
Differences from FIG. 9 are as follows. In this example, there is means 36 for storing a distribution ΔU (x) of dimensional variation of process non-uniformity obtained by experiments or the like.
[0101]
Further, the dimension variation Δ due to loading in the example of FIG. 9 is replaced with a dimension variation distribution ΔL due to loading.
[0102]
The loading correction circuit 37 is a dose DC for correcting the long-distance photosensitive action._fThe dose DC for correcting the long-distance photosensitivity of the sub-drawing region from the storage means 33 of the table (x) and the pattern density distribution table and the storage means 38 of the non-uniform dimensional variation distribution ΔU (x)._fExtract values of (x), pattern density, and non-uniform dimensional variation distribution ΔU (x).
[0103]
The loading correction circuit 37 has a function of calculating Δ (x) = ΔL (x) + ΔU (x). Based on the obtained Δ (x), s (Δ (x)), D (x), and the reference dose D₀From this, the corrected dose Da (x) is obtained.
[0104]
Although not explained so far, as is well known, the sign of Δ differs depending on whether positive or negative is used as a resist. It also varies depending on the etching process conditions.
As shown in FIG. 11A, a resist pattern 16 is formed by drawing and developing a pattern on the resist film 16 applied on the sample 13 using the pattern drawing method described above. The resist pattern 16 is a pattern in which the proximity effect, the long-distance photosensitive action, and the loading effect are corrected. Subsequently, as shown in FIG. 11B, the sample 13 is etched using the resist pattern 16 as a mask, and then the resist pattern 16 is removed, so that the dimensional variation caused by the etching is corrected with high accuracy. A pattern can be formed on the sample 13 (see FIG. 11C).
[0105]
Furthermore, this method can be applied to a transfer method using an electron beam. In the transfer method, the pattern is formed by irradiating the sample with a patterned electron beam obtained by scanning the pattern-formed mask while moving the electron beam continuously or on and off while stepping. Form. Again, by adjusting the current density of the scanning electron beam or the beam irradiation time, the distribution of the irradiation density on the sample can be distributed to correct the dimensional variation. Even when scanning is performed by moving in a stepwise manner, it is effective to maintain the continuity of the pattern by moving the beam positions in an overlapping manner.
[0106]
In the transfer method, the transfer pattern is often limited to a small area on the wafer, and a long-distance photosensitive action or loading effect or process non-uniformity may appear in a wider area than the area formed by one mask pattern. is there. In this case, when calculating the correction amount described above, the calculation is performed including the influence of adjacent patterns around the pattern data.
[0107]
In the above description, the description is limited to the drawing using the electron beam, but this can also be used in the drawing using the laser beam, for example. In this case, it is considered that the proximity effect and the long-distance photosensitive action are mainly caused by beam blurring or leakage beam in the optical system, but the dimensional variation caused by the process is the same as that by the electron beam. For example, the laser beam is turned on and off by using an acousto-optic device or the like, and the irradiation density of the laser beam is adjusted by adjusting the on time to correct the dimensional variation.
[0108]
【The invention's effect】
As described above in detail, according to the present invention, it is possible to correct a dimensional variation caused by etching with high accuracy.
[Brief description of the drawings]
FIG. 1 is a diagram showing a configuration of an electron beam drawing apparatus.
FIG. 2 is a cross-sectional view of a substrate for explaining a proximity effect.
FIG. 3 is a schematic diagram for explaining a long-distance photosensitive action.
FIG. 4 is a diagram illustrating a loading effect.
FIG. 5 is a diagram illustrating a conventional correction method for a loading effect.
FIG. 6 is a diagram showing an example of sample division in one embodiment of the present invention.
FIG. 7 is a diagram illustrating a loading effect correction method according to an embodiment of the present invention.
FIG. 8 is a flowchart showing a work flow in one embodiment of the present invention.
FIG. 9 is a flowchart showing a work flow in one embodiment of the present invention.
FIG. 10 is a flowchart illustrating a work flow according to the embodiment of the present invention.
FIG. 11 is a process cross-sectional view of a pattern forming method according to an embodiment of the present invention.
[Explanation of symbols]
1 electron gun
2 Converging lens
3 Molding aperture
4 Projection lens
5 Molding aperture
6 Forming deflector
7 Objective lens
8 Reticle Mask
9 High precision main deflector
10 High-speed sub deflector
11 Subfield
12 frames
13 samples
14 Incident electrons
15 Backscattered electrons
16 resist
17 Objective lens
18 Lower surface of objective lens
20 storage means
21 Memory means
22 Drawing system
23 Figure division circuit
24 Calculation means
25 Calculation means
26 Memory means
27 Long-distance photosensitivity correction calculator
28 Memory means
29 Proximity Effect Correction Operation Circuit
30 arithmetic circuit
31 Drawing circuit
32 Arithmetic circuit
33 Memory means
34 Proximity effect correction circuit
36 Memory means
37 Loading correction means
38 Memory circuit

Claims (8)

A pattern drawing method for drawing a pattern by irradiating an energy beam onto a sample coated with a resist,
Drawing data for drawing the pattern, a reference dose D ₀ for irradiating the energy beam, a pattern dependence distribution of a dimensional variation Δ due to the effect of the loading effect, and an energy distribution of the energy beam applied to the resist storing s;
Dividing the drawing area into a grid and forming a sub-drawing area;
Obtaining a pattern area density distribution for each of the sub-drawing regions based on the drawing data;
Calculating a dose DC _f (x) for correcting a long-distance photosensitive action in the sub-drawing region based on the pattern area density and the reference dose D ₀ ;
Calculating a dose DC _p (x) for correcting a proximity effect for a pattern in the sub-drawing region based on the drawing data and the reference dose D ₀ ;
A dose DC _f (x) for correcting the long-distance photosensitive action, a dose DC _p (x) for correcting the proximity effect, a pattern-dependent distribution of the dimensional variation Δ, and an energy distribution s of the energy beam Obtaining a dose D (x) based on:
Determining the irradiation position and shape of the energy beam based on data on the position and shape of the pattern in the sub-drawing region, and irradiating the energy beam for a time period corresponding to a dose D (x);
A pattern drawing method comprising: Obtaining a dimension variation distribution Δ (x) in each of the sub-drawing regions from the pattern area density distribution and a pattern dependence distribution of the dimension variation Δ due to the influence of the loading effect;
With
The dose DC _f (x) for correcting the long-distance photosensitivity is calculated based on the pattern area density distribution, the reference dose D ₀ , and the dimension variation distribution Δ (x).
The dose DC _p (x) for correcting the proximity effect is data relating to the position and shape of the pattern in the sub-drawing region, the reference dose D ₀ , the dimension variation distribution Δ (x), and the energy distribution of the energy beam. The pattern drawing method according to claim 1, wherein the pattern drawing method is calculated based on s. The dose D (x) is a product of a dose DC _p (x) for correcting the proximity effect and a dose DC _f (x) for correcting the long-distance photosensitivity. 3. The pattern drawing method according to 1 or 2. Dose DC f _(x) is a pattern drawing method according to claim 3, wherein the determining the dose D (x) embodied as the base dose D ₀ to correct the long-distance photosensitive action. The dose D (x) is: D (x) = DC _p (x) × DC _f (x) / (1+ (2s (Δ) −1) × (DC _p (x) × DC _f (x) / The pattern drawing method according to claim 1, wherein the pattern drawing method is obtained by D ₀ )).   6. The pattern drawing method according to claim 5, wherein the dimensional variation Δ includes a dimensional variation caused by non-uniformity of the etching rate of the resist in addition to a loading effect. Dose DC f _(x) is a pattern drawing method according to claim 5, wherein the determining the dose D (x) embodied as the base dose D ₀ to correct the long-distance photosensitive action. A step of drawing a pattern on the resist using the pattern drawing method according to claim 1, developing the resist, and forming a resist pattern;
Etching the sample using the resist pattern as a mask to form a pattern on the sample;
A pattern forming method comprising:

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