JP3034350B2 - Etching liquid flow simulation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for optimizing a spray amount distribution in an etching process of transporting a plate to be etched such as an iron plate through a chamber and spraying an etchant. The present invention relates to a simulation method for obtaining a quantity distribution.

[0002]

2. Description of the Related Art In general, when a shadow mask is manufactured, a plurality of chambers each having a plurality of banks provided with a plurality of nozzles are arranged in series and a steel plate is conveyed. An iron plate is uniformly pierced by spraying from the front side and the back side and performing an etching process.

[0003]

By the way, in the etching step for piercing an iron plate, if the liquid flow on the iron plate under spraying stagnates, the etching by the sprayed new highly corrosive etching solution is hindered. Therefore, the size of the holes in the shadow mask becomes uneven, and when the image is viewed through a CRT with a high-speed scanning line, the holes in the shadow mask become apparent and observed. This is considered to be one of the causes of the television failure, and it is extremely important to analyze the state of the stagnation of the etching solution on the iron plate in order to make the holes uniform.

[0004] However, it is difficult to accurately and quantitatively grasp the stagnation condition by experiment because the etching solution is extremely corrosive and the spray solution is extremely violently sprayed. In addition, the conventional fluid analysis strictly solves the Navier-Stokes equation, and must be calculated using a three-dimensional model.
In addition, since it is necessary to calculate each droplet, the analysis of the liquid flow under spraying in a considerably large area requires a huge amount of calculation exceeding the level of the current computer, and is actually difficult. .

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and a liquid capable of analyzing the state of stagnation of an etchant on an iron plate by reducing the number of meshes using a two-dimensional flow velocity vector and the thickness of the liquid. It is an object to provide a flow simulation method.

[0006]

According to the liquid flow simulation method of the present invention, a plate to be etched is conveyed through an etching chamber, and an etching target is sprayed from a plurality of nozzles attached to a swinging bank. This is an etchant flow simulation method that uses a computer to calculate the etchant flow on the processing plate, and calculates the liquid flow by referring to line specification data, etchant spray volume distribution data, and etchant pressure distribution data. Liquid flow calculation processing means for performing the calculation, and an output processing means for outputting the calculation result, wherein the liquid flow calculation processing means determines a target nozzle at which a point of interest on the plate to be etched enters the spray area. And a nozzle tip trajectory calculation processing section for obtaining the tip trajectory of the spray nozzle; From the liquid spray volume distribution data, a nozzle height, with the interpolation of nozzle pressure, spray amount distribution,
An interpolation processing unit that makes the compression pressure distribution continuous, and from the calculated nozzle tip trajectory, the interpolated spray volume distribution, and the compression pressure distribution, the oblique spray volume and the compression pressure distribution characteristics from the vertical spray volume and the compression pressure distribution characteristics. An oblique spray conversion processing unit to calculate, a spray amount calculating unit to calculate the spray amount at each point on the plate to be etched from the vertical spray amount distribution characteristics and the oblique spray amount distribution characteristics, and a vertical spray pressure. From the distribution characteristics and the oblique spray compression pressure distribution characteristics, the compression pressure calculation unit that calculates the compression pressure at each point on the plate to be etched, the spray amount calculation unit, and the processing target plate based on the calculation results of the compression pressure calculation unit It is characterized by comprising a supply momentum calculation unit for calculating the above supply momentum, and a liquid flow calculation unit for calculating a liquid flow from the supply momentum calculation result. Further, the present invention is characterized in that the liquid flow calculation unit calculates the two-dimensional flow velocity value on the plate to be etched and the thickness of the liquid.

[0007]

According to the present invention, the flow of the etchant on the plate to be etched is obtained by computer simulation. The data of the chamber configuration such as chamber arrangement, bank mounting position, nozzle pitch, nozzle height, etc. , Swing condition data such as nozzle swing angle, transfer condition data such as plate width, plate transfer speed, etc., and spray amount distribution and impact pressure distribution from one nozzle are experimentally obtained, and this data is read into a computer. With the nozzle's vertical spray characteristics, the spray characteristics at the time of swing are derived from the nozzle's vertical spray characteristics according to the oblique spray conversion rule.
The amount of spraying the etching solution and the pressure of the droplet at each point on the plate are determined to determine the momentum to be supplied onto the plate.
It is possible to calculate the dimensional flow velocity value and the thickness of the liquid, form an image, and easily know the liquid flow on the plate visually.

[0008]

Embodiments will be described below with reference to the drawings. First, the etching apparatus of the present invention will be described with reference to FIGS. In the figure, 10 is a chamber, 13 is a bank, 14 is a nozzle, 15 is a plate, 30 is a driving member, 31 is a push rod, 32 is a rod, 36 is a driven shaft, and 37 is a link.

FIG. 3 shows an example of a chamber.
A plurality of banks 13 made of thin tubes are provided in the transport direction on the front and back sides of a plate 15 such as an iron plate for a shadow mask to be etched through the chamber.
3 is provided with a plurality of nozzles 14. The plate 15 is transported at a constant speed in the direction of the arrow, and an etching solution is sprayed from a nozzle in the chamber 10 to be etched.

The swing of the bank 13 is as follows. That is, as shown in FIG. 4, the rotation of the drive member 30 causes the end of the push rod 31 fixed to the drive member to rotate, and as a result, the rod 3 connected to the push rod 31
2 swings left and right. Since the link 37 is rotatably attached to the rod 32, the rod 32 moves to the left and right, and additionally moves up and down. This rod 32 causes the link 37 to swing right and left, and the driven shaft 3
By rotating the nozzle 6 by a predetermined angle, the bank 13 connected to the driven shaft 36 is rotated to swing the nozzle at a predetermined swing angle.

As described above, it is extremely important to check the flow of the liquid at each point of the plate when the etching liquid is sprayed on the plate being conveyed while shaking the nozzle. However, the etching liquid is extremely corrosive. , It is extremely difficult to put the measuring instrument in the chamber for measurement. Therefore, in the present invention, the liquid flow is obtained by simulation by a computer.

FIG. 1 is a diagram showing an overall configuration of a simulation system according to the present invention, and FIG. 2 is a diagram showing a hardware configuration. In the figure, 01 is the spray amount nozzle distribution data, 02 is the pressure distribution nozzle distribution data, 03 is the line specification data, 04
Is spray experiment data, 05 is liquid flow calculation processing means, 05
1 is a spray amount calculation unit, 052 is a pressing force calculation unit, 053 is a supply momentum calculation unit, 054 is a liquid flow calculation unit, 055 is a nozzle tip orbit calculation unit, 056 is an interpolation processing unit, 057 is a target nozzle determination processing unit, Reference numeral 058 denotes an oblique spray conversion processing unit, 06 denotes an output unit, 07 denotes a CPU, 08 denotes a main memory, 09 denotes an output device, 010 denotes an input device, and 011 denotes an external storage device.

The line specification data 03 mainly includes chamber configuration data, swing condition data, and transfer condition data. As shown in FIG. 5A, the chamber configuration data includes the number of chambers arranged, the width w of the chamber, the length L of the chamber, the depth P from the level of the plate to be etched to the bottom of the chamber, and the level of the plate to be etched. From the height H to the top of the chamber, and the mounting position of the bank (X, Y,
Z), nozzle pitch P, nozzle height NH, nozzle characteristics T, nozzle length NL, nozzle vane angle θ, and the like.

The swing condition data includes a rotation speed ω, a nozzle swing angle α, and the like as shown in FIG. 5B, and the transfer condition data is etched as shown in FIG. 5C. Plate width W, transfer speed V, plate end point coordinates (X, Y)
And so on.

[0015] Spray amount calculation unit 051, impact pressure calculation unit 052
Reads the line specification data and reads the spray amount nozzle distribution data and the compression nozzle distribution data to calculate the spray amount and the compression pressure. At this time, the processing of the nozzle tip orbit calculation unit 055 and the interpolation processing unit 056 is performed. Based on the result, the target nozzle at each point determined by the target nozzle determination processing unit 057 and the conversion amount at each point converted by the oblique spray conversion processing unit 058 are read to calculate the spray amount and the compression pressure.

Here, the processing of the nozzle tip trajectory calculation processing unit 055 will be described below in the case where a swinging system as shown in FIG. 4 is used. When the rod 32, one end of which is connected to the push rod 31 whose end point rotates by the rotation of the driving member 30, reciprocates left and right while moving up and down, the link 37 swings left and right to rotate the driven shaft 36. By doing so, the bank is rotated, and the nozzle attached to the bank is swung. Now, as shown in FIG. 6, the horizontal distance between the center of the drive side and the swing center of the swing member is D, the length of the push rod 31 is 1 and the length of the rod 32 is L. The height is H, the turning radius of the link 37 is R,
Assuming that the rotation radius of the drive point Q of the push rod driven by the drive member 30 is r, the rotation angle on the drive side is φ, and the swing angle on the nozzle side is χ, Rcosχ = H + rcosφ− [l ² − ｛(D −L) + Rsinχ−rsinφ｝ ² ] ^1/2 holds. Solving this for χ, here, A A = 2 (HR + rRcosφ) B = 2 {rRsinφ- (D-L) R} C = R 2 + r 2 + H 2 + (D-L) 2 -l 2 + 2Hrcosφ-2 (D-L) rsinφ.

By obtaining χ from these equations, the motion state of the link 37 can be known, so that the tip trajectory of the nozzle 14 of the bank connected to the driven shaft 36 rotated by this can be obtained. The interpolation processing unit 056 performs an interpolation process for the nozzle height and the spray pressure from the line specification data and the spray experiment data, and performs an interpolation process for making the spray amount distribution and the impact pressure distribution continuous.

The spray experiment data 04 indicates that when the nozzle 14 to be used is determined, the nozzle 14 is set at a certain height,
As shown in FIG. 7A, the amount of liquid at each point when the spray is sprayed vertically downward for 20 to 30 seconds using the cell 40 subdivided into a predetermined number is obtained by an experiment. At this time, the liquid amount at each point is obtained by changing the height of the nozzle and the spray pressure, and is stored as spray experiment data. Further, as shown in FIG. 7B, the nozzle 14 is set at a fixed height, and
While moving the pressure sensor 41 installed on the stage 43 in the X and Y directions as indicated by arrows, the spray is sprayed vertically downward from the nozzle 14, and the pressure at each point is obtained by experiment, and the obtained data is obtained. Is stored in a personal computer (or data recorder) 42, for example. At this time, the impact pressure at each point is obtained by changing the height of the nozzle and the spray pressure, and stored as spray experiment data.

In the interpolation process, when the actually measured distributions 50 and 51 as shown in FIG. 8 are given by the spray experiment data, the expected distribution 52 when the nozzle height and the spray pressure are changed.
Is obtained by interpolation, and the actually measured distribution and the predicted distribution have a stepwise distribution. Therefore, the distribution is made continuous so as to be suitable for the spray amount calculation processing and the pressing pressure calculation processing, and the distribution 5 is obtained.
The processing for obtaining 3, 54, 55 is performed.

The interpolation process for making the distribution continuous is performed by linearly approximating each section, or by approximating a quadratic curve, a cubic curve, or the like. Interpolation processing relating to the nozzle height, for example, as shown in FIG. 9, when the value of the height H ₁ is given as an experimental value, spray volume distribution to the height H ₂ is the height for small solid angle dω and the spray amount of the area S ₁ of the H _1, as is equal to the amount of spray in the area S ₂ at the height H _2, and requests the distribution of H _2.

In the pressure interpolation processing, for example, as shown in FIG. 10, the spray amount with respect to the pressure is given as experimental data such as P ₁ , P ₂ , P ₃ , P ₄ , P ₅ , P ₆ . Sometimes, the spray amount during that time is interpolated by connecting each point with a cubic curve.

When the nozzle tip trajectory is obtained in this way and interpolation processing is performed, first, a nozzle to be sprayed is determined for each point of the plate conveyed by the target nozzle determination processing unit 057. The determination of the target nozzle at each point on the plate is roughly divided into a narrowing of the nozzle at a position in the traveling direction of the plate and a strict determination for the narrowed nozzle.
Performed by two processes.

Usually, a plurality of chambers each including a large number of nozzles are arranged in series in one etching line, and when all of them are summed up, an enormous number of nozzles swing. Therefore, if strict object determination is performed for all nozzles, the processing becomes enormous.

Therefore, before the strict object determination, the number of nozzles is first narrowed down to some extent. That is, since all the nozzles are reciprocating periodically, a range in which the liquid can be sprayed on the plate for each nozzle can be specified, for example, as shown by a rectangle 60 in FIG. .
The rectangle 60 is a rectangle that can cover the entire range sprayed when the nozzle is shaken left and right, and the spray area below vertically is small, and when shaken maximally, the area sprayed because the liquid spreads is wide. Become.

As described above, the range in which the liquid is sprayed for each nozzle is determined for the traveling direction of the plate, and from these values,
As shown in FIG. 12, a range in the plate advancing direction in which the nozzle must be provided because the liquid is sprayed on the point of interest P is obtained. It is determined for each nozzle whether or not the nozzle falls within this range. For example, FIG. 12 shows that two nozzles marked with “〇” correspond.

The size of the range for determining the point of interest only needs to be determined once, and the number of strict determinations required by this process depends on the bank configuration.
You can narrow down to zero.

Next, a strict determination of the target nozzle with respect to the narrowed nozzle is performed. Here, it is assumed that the spray area by the nozzle is defined as a rectangular area. When the nozzle is swung, the size of the assumed rectangular area changes according to the swing angle.
It is determined whether or not the point of interest falls within one of the two endpoints. This is because when the point of interest is inversely transformed by the swing angle and moved vertically downward, the rectangular area below the vertical This is equivalent to determining whether or not to enter.

Now, as shown in FIG. 13, the point of interest is P, the vector indicating the direction of the point of interest P from the spray port of the nozzle is (α _x , α _y , α _z ). The vector indicating the spray axis is (t _x , t _y , t _z ), and the vector indicating the direction of the point of interest from the spray port when the oblique spray axis is vertically downward is (β _x , β _y , β _z ). And a unit vector indicating a vertically downward (or upward) (0,0, epsilon) (where ε = ± 1) and then, the orthonormal system is translating the origin to the nozzle pivot center (e _x, e _y,
ez ), the transformation matrix T is as shown in equation (1).

[0029] It is.

The vector (β _x ,
β _y , β _z ) The point of intersection P (Q _x , Q _y , Q _z ) between the extension of
It is sufficient to determine whether or not this point is within the spray rectangular area of the nozzle. However, since the nozzle is actually rotated by the vane angle of the nozzle, the rectangle for determining whether Q (Q _x , Q _y , Q _z ) is the target is oblique.

The determination as to whether or not the object is within the rectangular area
For example, as shown in FIG.
The sum of the angles θ ₁ , θ ₂ , θ ₃ , and θ ₄ formed by the line segments connecting the point and the four end points (C ₁ , C ₂ , C ₃ , C ₄ ) of the rectangular area is obtained. As shown in (a), if it becomes 2π, it can be determined that the point is within the rectangle.
If the sum of θ ₁ , θ ₂ , θ ₃ , and θ ₄ becomes 0 as shown in FIG. 4B, it can be determined that the point is outside the rectangle.

The nozzle 1 thus narrowed down in advance
The target nozzle can be determined by performing strict determination processing for each one. Next, the conversion process of the oblique spray conversion processing unit 058 will be described. In the oblique spray conversion process, the spray amount distribution 60 in the vertically downward stationary state received from the interpolation processing unit 056 as shown in FIG.
Based on the nozzle swing characteristics received from the nozzle orbit tip processing unit 055, the spray amount distribution 61 at the time of swing as shown in FIG. 15B is converted. Are assumed to be equal, and the height of the distribution is determined from the area ratio.

Now, as shown in FIG. 16A, R is the distance from the center of the bank to the nozzle tip, H is the distance between the nozzle tip and the plate surface in vertical spraying, and H 'is the nozzle in oblique spraying. Distance between tip and plate surface, θ is bank swing angle, φ is angle between spray axis and droplet ejection direction, η is angle between swing direction and plate width direction, ψ is spray direction and plate advancing direction The angle between the spray direction at the time of oblique spraying and the Z axis (vertical direction);
dω is the minute solid angle at the time of vertical spraying, dω 'is the minute solid angle at the time of oblique spraying, v is the average velocity of the droplets, μ is the droplet space occupancy at the time of vertical spraying, and μ' is the minute solid angle at the time of oblique spraying. Droplet space occupancy, d
F is the amount of liquid sprayed through the minute solid angle dω per unit time, ρ is the liquid density, and dt is the minute time.

Now, in order to obtain the spray amount for the small solid angle dω at the angle φ between the spray axis and the droplet discharge direction in the vertically downward spray, as shown in FIG. Is vdt, area d perpendicular to spray direction
Considering the space consisting of S, similarly, at the bank swing angle θ, the length vdt and the area dS ′ perpendicular to the spray direction at a small solid angle dω at an angle φ between the oblique spray axis direction and the droplet ejection direction. Considering the following space, dS: dS ′ = H ² sec ² φ: H ′ ² sec ² … (3) The amount of droplets in this volume is Becomes

Next, as shown in FIG. 16 (d), considering a space which is cylindrical along the spray direction and whose upper and lower sides are parallel to the surface of the plate, the spray amount Holds.

From these (3) to (5) Is obtained.

In this way, the conversion formula between the vertically downward spray and the oblique spray is obtained, so that the oblique spray amount at the time of swing can be calculated from the vertically downward spray characteristic from the interpolation processing unit 056.

Next, the spray amount calculation unit 051 calculates the spray amount for each point of interest from the determined target nozzle and the oblique spray conversion characteristics.

As shown in FIG. 17, when the spraying of the nozzles 14-1, 14-2,..., 14-7 is considered as shown in FIG. -3, 14
Assuming that the nozzles -4 and 14-5 are the target nozzles, the spray amount at the point of interest P is calculated based on the spray characteristics obtained by the oblique spray conversion.
The spray amount is calculated for one nozzle, the spray amount is calculated as the sum of the spray amounts from each nozzle, and the spray amount is calculated for each point of interest every moment.

Next, the processing in the pressing force calculation unit 052 will be described. m is the average droplet mass, N is d during time dt
Assuming that the total number of droplets passing through S and N ′ is the total number of droplets passing through dS ′ during time dt, Holds.

Now, assuming that k is a virtual elastic coefficient, λ is a unit vector indicating an incident direction, and ξ is a vector indicating a virtual direction of momentum, mvλ · N = kmv · ξ · N + dP (8) holds. I do. That is, the left side is the total momentum of the droplet sprayed on the plate, and the first term on the right side is the total momentum of the droplet after colliding with the plate. Therefore, the difference is the droplet pressing pressure dP.

When λ = (λ ₁ , λ ₂ , λ ₃ ) and ξ = (ξ ₁ , ξ ₂ , ξ ₃ ,), the component perpendicular to the plate surface in the equation (8) is given by mv · λ a _{3 · N = kmvξ 3 N +} dP.

[0043] Here, the k · ξ ₃ and reservoir new K (v,
Assuming λ ₃ ),

DP = mvλ ₃ NK (v, λ ₃ ) · mvN λ ₃ corresponding to dS is cosφ, and λ ₃ corresponding to dS ′ is
cosχ, dP = mvN ｛cosφ−K (v, cosφ)｝ dP ′ = mvN ｛cosχ−K (v, cosχ)｝ (9) Eliminating mvN with this equation gives It becomes an expression. Therefore, The pressure conversion formula is obtained as

Here, since v can be considered to be determined by the type of nozzle and its pressure, if the type of nozzle is fixed, K can be regarded as a function of pressure P instead of v, and therefore K (p,
cosφ). Function K (p, cos
φ) can be obtained from the experimental values by multiple regression analysis.

However, sometimes cosχ−K (p, cos
χ) and cosφ−K (p, cosφ) both approach 0, so that the value of dP ′ may not be determined accurately. _{Here, F P (θ, χ,} η) I + 2J + 2L + 2 = Σ Σ Σβ ijl N ik (θ) N jk (φ) N lk (cosη) i = 0j = 0l = 0 I + 2J + 2L + 2 + Σ Σ Σγ ijl N ik (θ ) N _jk (φ) N _lk (sin η) i = 0j = 0l = 0 (N _ik , N _jk and N _lk are k-th order B splines)
Thus, β _ijl and γ _ijl are determined by multiple regression analysis.

Thus, the pressing pressure conversion formula uses the above F _P , It can be expressed as.

In this way, a conversion formula between the vertically downward spray and the oblique spray is obtained. Next, from the determined target nozzle and the oblique spray conversion characteristics, a droplet hitting pressure is calculated for each point of interest. The droplet impact pressure calculation process is similar to the case of the spray amount calculation,
As shown in FIG. 17, when considering the spraying of the nozzles 14-1, 14-2,..., 14-7, the nozzles 14-2, 14-3, 14-4, 14- with respect to the point of interest P at a certain time. Assuming that 5 is the target nozzle, the point of interest P is determined from the spray characteristics obtained by the oblique spray conversion.
Is calculated for each of the four nozzles, and as a total sum of the pressures applied by spraying from the nozzles, the pressure is calculated momentarily for each point of interest.

Next, the processing of the supplied exercise amount calculation unit 053 will be described. The pressing force value obtained by the above-described pressing force calculation processing includes only a vertical component. Therefore, this value cannot be directly adopted as the momentum supply amount to the liquid flow. Therefore, the amount of momentum supplied to the liquid flow is evaluated by introducing the virtual elastic coefficient introduced when the pressure conversion formula was derived.

In equation (8), mvλN is the momentum of the incident droplet, kmvξ is the momentum other than dp, that is, the momentum supplied to the liquid flow by droplet incidence, and dp is the pressure applied to the plate surface. It is. Therefore, to obtain the momentum supply amount to the liquid flow, kmvｋN may be obtained.
The equation (8) is separated for each component, and mvλ ₁ N = kmvξ ₁ N (12) mvλ ₂ N = kmvξ ₂ N (13) mvλ ₃ N = kmvξ ₃ N + dp (14) (Λ ₁ , λ ₂ , λ ₃ ) is a unit vector representing the incident direction of the droplet, and (ξ ₁ , ξ ₂ , ξ ₃ ) is a unit vector representing the moving direction of the liquid flow.

[0051] With additional put K = kξ _3, (1
From equation 4) Get. Substituting this into the equations (12), (13), and (14), the momentum supply amount of the liquid inflow is calculated using K corresponding to the virtual elastic coefficient. Can be expressed as Here, the swing correction function F
The value of K is obtained using _P (θ, χ, η). θ, χ, η
Is the swing angle of the spray nozzle with respect to the vertical line, χ is the angle of the spray center axis with respect to the vertical line, and η is as shown in FIG. 18 (a) (side view) and FIG. 18 (b) (top view), respectively.
Is the angle of the spray nozzle swinging direction with respect to the plate advancing direction (x direction).

First, as shown in FIG. 19, a relational expression between the swing correction function and the virtual elastic coefficient when the target droplet orbit is taken in the direction of the spray center axis and the nozzle is sprayed obliquely by ψ. From Is obtained. Equation (17) is based on the case where the spray direction is vertical and the focused jet flight direction is the spray center axis direction.
This is a correction function in the case of (oblique) the flight direction of the target liquid jet is the spray center axis. Where F _P (ψ, 0, η) is ψ = 0
°, 5 °, 10 °, 15 °, etc., are determined by the least-squares method from the values determined experimentally. Thus, F _P (ψ,
Once (0, η) is obtained, if K (p, cos0) is known, the value of K (p, cosψ) can be obtained from the value of F _P (ψ, 0, η).

First, the value of K (p, cos0) is determined.
This represents the case where the droplet is incident perpendicularly to the plate surface. In this case, the momentum supply amount is expressed as λ in Expression (16).
= (0,0,1) Becomes Therefore, although the momentum supply in the x and y directions should be 0, in reality, the liquid is also isotropically pushed out in the x and y directions, and the momentum supply in the x and y directions is performed. here,
The momentum supply is evaluated using a simplified model as described below.

FIG. 20 is a diagram for explaining the distribution of the supply momentum in the vertical direction in the horizontal direction. As shown in FIG. 20A, a liquid 71 having a volume df is added to the still water surface having a surface height h, and as a result, as shown in FIG. It is assumed that the liquid that has been extruded isotropically and that is in front of the extruded point is lifted upward. At this time, the momentum generated in the x and y directions is the momentum of the liquid extruded in the horizontal direction, and the sum of the absolute values is assumed to be equal to the third component in the equation (18). That is, assuming that the momentum in the vertical direction is simply distributed in the same direction on the x and y planes, assuming that the flow velocity of the extruded liquid is v, πv ² h = df (19) From this, v is given by: v = (df / πh) ^1/2 (20), and if the momentum of the liquid 71 is equal to the third component of the equation (18) using this v, Is obtained. From this, when K (p, cos0) is obtained, Is obtained. Substituting this into equation (17) to determine the virtual elastic modulus gives K (p, cosψ) Substituting λ ₃ = cosψ into this, By substituting the equation (22) into the equation (16), the momentum supply amounts are all represented by known quantities.

Next, the processing of the liquid flow calculation unit 054 will be described. By the way, since the expression (16) includes the third component (rebounded in the z-axis direction), it is necessary to distribute this in the x and y directions. Therefore, as shown in FIG. 21, this is equally distributed to a simplified orthogonal mesh.

First, the balance of the flow rate is shown by (x
Consider a control volume (hereinafter CV) centered on _i , y _j ). In FIG.
The boundary of V is shown. The inflow / outflow of liquid in this CV can be classified into the following two types.

(A) Replenishment of liquid by spraying (b) Outflow / inflow of liquid from CV boundary In the following, the following symbols are used.

F (x, y, t): spray amount per unit time, unit area v _x (x, y, t): average velocity in the x direction on the plate surface v _y (x, y, t) ) y-direction average flow rate h (x on ...... plate surface, y, t) ...... liquid level function p _x (x representing the height, y, t) ...... spraying unit time supplied by the unit area Momentum in x direction per unit _py (x, y, t)... Momentum in y direction per unit time and unit area supplied by spray atomization The balance equation is as follows.

[0059] Similarly, a balance formula is used for the momentum. However, here, the acceleration that causes the liquid flow caused by the difference in liquid level is compared with the difference in liquid level, and the area force and gravity caused by viscosity on the boundary surface of the CV are: F = (Fx,
Fy). Let ρ be the liquid density and k be the proportional coefficient of acceleration caused by the difference in liquid level.
The balance formula is A balance equation for the y-direction momentum can be derived in a similar manner.

Based on these balance equations, ΔxΔ
By taking the limit by dividing the sides people in yΔt, basic equations ∂h / ∂t = f-∂ ( v x h) / ∂x-∂ (v y h) / ∂y ...... (25) ρ∂ ( _{v x h) / ∂t = p} x -ρ∂ (v x 2 h) / ∂x -ρ∂ (v x v y h) / ∂y + k∂h / ∂t + F x ...... (26) ρ∂ (v _{y h) / ∂t = p y} -ρ∂ (v y 2 h) / ∂x -ρ∂ (v x v y h) / ∂y + k∂h / ∂y + F y ...... (27) is obtained.

These equations can be discretized and solved by the finite difference method. At this time, if an orthogonal mesh is used as shown in FIG. 21, a vibration equal to the mesh interval is generated. In order to suppress this vibration, a mesh system in which the meshes of the flow velocity and the liquid thickness are shifted as shown in FIG. 22 may be used. In FIG. 22, ○ indicates a mesh of flow velocity, momentum and impact pressure, and ● indicates a mesh of liquid thickness and spray amount.
Indicates the point of interest [i, 2j-1], and FIG. 22B indicates that the point of interest is [i, 2j]. Discrete using this mesh system,
The value between meshes can be solved by performing average approximation using the predictor-corrector method for the time progress. Then, the nozzles are arranged in a quasi-lattice or zigzag pattern, and a swing angle of 7, a vibration speed of 50,
When the liquid flow at a nozzle end pressure of 3 kg / cm ² was determined, almost satisfactory results were obtained.

The output processing means 06 converts the liquid flow data obtained for each point of interest into an image and outputs the data.
For example, the liquid thickness is represented as image data having a density of 16 gradations, and the liquid flow is represented by an arrow. In this case, the expression may be a monochrome gradation expression or a color image gradation expression. In this way, the image-processed data is displayed on the output device 09 such as a CRT or printed out by a printer such as a sublimation transfer, so that the liquid flow on the plate can be known at a glance.

In the simulation method of the present invention, as shown in FIG. 2, each module of a program constituting each processing unit of the liquid flow calculation processing means 05 is stored in an external storage device 01.
1 is read by the CPU 07, the spray amount nozzle distribution data, the compression nozzle distribution data, and the line specification data are read into the main memory 08 to perform the above-described processing, and necessary data are appropriately input by the input device 010. At the same time, the processing results are imaged or printed out from the output device 09.

[0064]

As described above, according to the present invention, the droplets are not treated one by one, but the spray amount supplied per unit area per unit time and the momentum in the x and y two-dimensional directions are averaged. By calculating the liquid level and the liquid level at the same time, the equation to be satisfied by the two-dimensional flow velocity vector and the liquid thickness is determined, the number of meshes is reduced, and the calculation can be performed at the current computer level.

[Brief description of the drawings]

FIG. 1 is a diagram showing an overall configuration of a simulation system.

FIG. 2 is a diagram showing a hardware configuration of a simulation method.

FIG. 3 is a schematic diagram of an etching apparatus.

FIG. 4 is a diagram showing a bank swing system.

FIG. 5 is a diagram showing a data configuration.

FIG. 6 is an explanatory diagram of swing analysis.

FIG. 7 is a diagram for explaining a method for obtaining spray experiment data.

FIG. 8 is a diagram illustrating an interpolation process.

FIG. 9 is a diagram for explaining an interpolation processing method relating to height.

FIG. 10 is a diagram for explaining an interpolation processing method for pressure.

FIG. 11 is a diagram for explaining target nozzle determination processing.

FIG. 12 is a diagram for explaining target nozzle determination processing.

FIG. 13 is a diagram for explaining target nozzle determination processing.

FIG. 14 is a diagram for explaining oblique spray conversion.

FIG. 15 is a diagram for explaining oblique spray conversion.

FIG. 16 is a diagram illustrating calculation of a spray amount / compression pressure value at a point of interest.

FIG. 17 is a diagram illustrating calculation of a spray amount / a compression pressure value at a point of interest.

FIG. 18 is a side view and a top view at the time of spraying.

FIG. 19 is a diagram illustrating a method of calculating a virtual elastic coefficient.

FIG. 20 is a diagram illustrating the distribution of the supply momentum in the vertical direction in the horizontal direction.

FIG. 21 is a diagram showing an orthogonal mesh.

FIG. 22 is a diagram illustrating a method of setting an orthogonal mesh for suppressing vibration.

[Explanation of symbols]

01: spray amount nozzle distribution data, 02: compression nozzle distribution data, 03: line specification data, 04: spray experiment data, 05: liquid flow calculation processing means, 051: spray amount calculation unit, 052: compression pressure calculation unit, 053: supply momentum calculation unit, 054: liquid flow calculation unit, 055: nozzle tip trajectory calculation unit, 056: interpolation processing unit, 057: target nozzle determination processing unit, 058: oblique spray conversion processing unit, 06: output unit 0
7 CPU, 08 main memory, 09 output device, 010
... input device, 011 ... external storage device.

──────────────────────────────────────────────────続 き Continued on front page (58) Field surveyed (Int. Cl. ⁷ , DB name) C23C 1/00-1/08 G06F 17/00

Claims (2)

(57) [Claims] 1. An etching process in which a plate to be etched is conveyed through an etching chamber and a liquid flow of the etching solution on the plate to be etched in an etching process in which an etching solution is sprayed from a plurality of nozzles attached to a swing bank is calculated by a computer. An etching liquid flow simulation method obtained by simulation, wherein liquid flow calculation processing means for calculating a liquid flow with reference to line specification data, etching liquid spray amount distribution data, and etching liquid impact pressure distribution data, and outputs a calculation result. An output processing means, wherein the liquid flow calculation processing means comprises: a target nozzle determination processing section for determining a target nozzle at which a point of interest on the plate to be etched enters the spray area; and a nozzle tip trajectory for obtaining a tip trajectory of the spray nozzle. Compute nozzle height and nozzle pressure from the calculation processing unit and the etchant spray amount distribution data. While the spray volume distribution,
An interpolation processing unit that makes the compression pressure distribution continuous, and from the calculated nozzle tip trajectory, the interpolated spray volume distribution, and the compression pressure distribution, the oblique spray volume and the compression pressure distribution characteristics from the vertical spray volume and the compression pressure distribution characteristics. An oblique spray conversion processing unit to calculate, a spray amount calculating unit to calculate the spray amount at each point on the plate to be etched from the vertical spray amount distribution characteristics and the oblique spray amount distribution characteristics, and a vertical spray pressure. From the distribution characteristics and the oblique spray compression pressure distribution characteristics, the compression pressure calculation unit that calculates the compression pressure at each point on the plate to be etched, the spray amount calculation unit, and the processing target plate based on the calculation results of the compression pressure calculation unit An etching liquid flow simulation method comprising: a supply momentum calculation section for calculating the supply momentum; and a liquid flow calculation section for calculating a liquid flow from the supply momentum calculation result. 2. The etching liquid flow simulation method according to claim 1, wherein the liquid flow calculation unit calculates a two-dimensional flow velocity value on the plate to be etched and a liquid thickness.