JPH09274307A - Circuit pattern dividing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce load on the design of a reticle by dividing a circuit pattern so that at least a part of a display part and a part of a conduction part may be included in one division area. SOLUTION: The circuit pattern 20 is provided with eight lead wire groups 22 at the 1st and the 2nd ends 21A and 21B of a periphery part 21, and four lead wire groups 23 at the 3rd end 21C thereof. The circuit pattern 20 is divided into two in an orthogonal direction to a longitudinal direction so that the 1st and the 2nd ends 21A and 21B may make four lead wire groups 22 one pattern. The respective blocks are divided into two so that the 1st end 21A and the 2nd end 21B may make three lead wire groups 22 one pattern on the central part side of each circuit pattern 20. Next, the circuit pattern 20 is divided in the longitudinal direction so that the 3rd end 21C may make two lead wire groups 23 one pattern. Then, the circuit pattern 20 is divided into eight division patterns 12A to 12F.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a circuit pattern dividing method, for example, a liquid crystal display (LCD).
It is suitable to be applied to a circuit pattern dividing method for dividing a circuit pattern of l Display).

[0002]

2. Description of the Related Art In recent years, liquid crystal displays have been widely used as display elements for personal computers and television receivers. Conventionally, in this liquid crystal display, a glass substrate on which a desired circuit pattern is patterned by a photolithography method is used.

A projection type exposure apparatus is usually used in the exposure step for patterning a circuit pattern on the glass substrate. In this exposure apparatus, exposure light emitted from a light source is applied to a reticle on which a circuit pattern of a liquid crystal display is formed, and a projection image of the circuit pattern obtained by the exposure light passing through the reticle is projected by a projection optical system. It is designed such that the resist film provided on the glass substrate can be projected through it, and thereby the resist film on the glass substrate can be exposed according to the exposure pattern.

In this case, as shown in FIG. 3, the circuit pattern 1 of the liquid crystal display has, for example, a rectangular shape and comprises a display portion 2 and a peripheral portion 3 formed so as to surround the display portion 2. . The display unit 2 has a pattern in which a plurality of electrodes corresponding to a plurality of red, green, and blue pixels are regularly arranged. In addition, the peripheral portion 3 includes, for example, a plurality of trapezoidal conductive portions (hereinafter, referred to as lead wires) formed of a plurality of lead wire patterns that electrically connect a pattern of each electrode and a plurality of driver circuits (not shown) that drive these electrodes. Called group) 4.

By the way, recently, a large area of the liquid crystal display is required. Accordingly, the size of the circuit pattern 1 of the liquid crystal display is the size of the effective diameter of the projection optical system of the exposure apparatus described above and the size of the surface on which the circuit pattern of the reticle is formed (hereinafter, these sizes will be referred to as If it is larger than the effective field), it is divided into a plurality of types of patterns according to the effective field.
Therefore, in this case, each pattern formed by dividing the circuit pattern (hereinafter, referred to as a division pattern) is formed on each of a plurality of reticles, and each division pattern formed on each reticle using an exposure apparatus is used. By projecting each onto a predetermined position on the glass substrate, the resist film on the glass substrate can be exposed according to the circuit pattern 1.

First, as shown in FIGS. 4A and 4B, when the circuit pattern 1 of the liquid crystal display has a size substantially equal to the size of the effective field, the circuit pattern 1 concerned. (Fig. 4
(A)), this circuit pattern 1 is formed on the reticle 5 (FIG. 4 (B)). Therefore, in the exposure apparatus, the resist film on the glass substrate is exposed according to the circuit pattern 1 by performing one exposure process using the reticle 5.

By the way, as shown in FIGS. 5A and 5B, the circuit pattern 1 of the liquid crystal display has a size equal to or larger than the effective field and up to about twice the size of the effective field. In this case, the circuit pattern 1 is divided into two, that is, a divided pattern B and a divided pattern C according to the effective field (FIG. 5A), and these divided patterns B and C are formed on the reticles 6A and 6B, respectively. (FIG. 5 (B)).

In this case, in the exposure apparatus, for example, the reticle 6A is first used to project the divided pattern B of the left half of the circuit pattern 1 on the resist film on the glass substrate, and then the reticle 6B is used to project the divided pattern B on the glass substrate. The remaining right half divided pattern C of the circuit pattern 1 is projected on the resist film. Thus, in the exposure apparatus, the reticle 6A
And 6B are used to expose the resist film on the glass substrate according to the circuit pattern 1 by performing the exposure process twice.

As shown in FIGS. 6A and 6B,
If the circuit pattern 1 of the liquid crystal display is more than twice the size of the effective field and has a size up to about 4 times the size of the effective field, the circuit pattern 1 is divided according to the effective field. 4 of pattern D, divided pattern E, divided pattern F and divided pattern G
(FIG. 6A), and these division patterns D to G
Are formed on the reticles 7A, 7B, 7C, and 7D, respectively (FIG. 6B).

Therefore, in the exposure apparatus, for example, the reticle 7A is first used to project the division pattern D on the upper left of the circuit pattern 1 onto the resist film on the glass substrate, and then the reticle 7B is used to project the resist film on the glass substrate. On the upper right of the circuit pattern 1 is projected onto the resist pattern on the glass substrate by using the reticle 7C, and then the lower left divided pattern F of the circuit pattern 1 is projected onto the resist film on the glass substrate. Finally, the reticle 7D is used to project onto the glass substrate. The division pattern G on the lower right of the circuit pattern 1 is projected on the upper resist film. Thus, in the exposure apparatus, the resist film on the glass substrate is exposed according to the circuit pattern 1 by performing the exposure process four times using the reticles 7A to 7D.

[0011]

When the circuit pattern 1 of such a liquid crystal display has a size four times or more the size of the effective field, the circuit pattern 1 is displayed on the display unit according to the effective field. 2 and surrounding area 3
And the display unit 2 and the peripheral unit 3 are finely divided. For example, as shown in FIG. 7A, in the circuit pattern 1 of the liquid crystal display, the display section 2 is divided into six substantially evenly. In this case, in the display unit 2, since the pattern of each electrode is relatively small and the electrodes are regularly arranged according to each pixel, the electrodes are divided into six divided patterns H having substantially the same pattern.

In the peripheral portion 3, the circuit pattern 1
The respective end portions (hereinafter, referred to as first and second end portions) 3 </ b> A and 3 </ b> B extending along the longitudinal direction (hereinafter, simply referred to as “longitudinal direction”) are divided into three substantially evenly. The respective end portions extending along the direction orthogonal to the longitudinal direction (hereinafter, these are referred to as third and fourth end portions) are substantially equally divided into two. In this case, in the peripheral portion 3, since the pattern of each lead wire of the lead wire group 4 is relatively larger than the pattern of each electrode of the display portion 2, the peripheral portion 3 is a boundary portion between adjacent lead wire groups 4. It is difficult to divide with
One lead wire group 4 is divided into two. Therefore, in the peripheral portion 3, each division pattern I, J, K, L, M,
The types increase as the patterns in which N, O, P and R are different from each other.

Therefore, as shown in FIG. 7B, when each of these divided patterns HR is formed on the reticle 8, the area of the surface of the reticle 8 on which the divided patterns HR are formed is effective. The divided pattern H is formed on the reticle 8A so that the divided circuit patterns I to K, L to N, and 0 to R are formed on the reticle 8B, 8C, and 8D, respectively. This reduces the number of reticles 8A to 8D required for a plurality of types of division patterns H to R.

By the way, in the exposure using the reticles 8A to 8D, the exposure process is first repeated six times using the reticle 8A, for example, to repeat the exposure process six times on the glass substrate according to the display portion 2 of the circuit pattern 1. The circuit pattern 1 is formed by exposing the resist film to light and then performing the exposure process 10 times by sequentially using the reticles 8B to 8D and covering the divided patterns other than the division pattern necessary for the exposure process with the light-shielding band.
The resist film on the glass substrate is exposed according to the peripheral portion 3 of. However, when the circuit pattern 1 of the liquid crystal display has a size of four times or more the size of the effective field as described above, when the size of the circuit pattern 1 is smaller than four times the size of the effective field. Compared with this, the number and types of the division patterns I to R are significantly increased, and accordingly, the number of exposure processes in the exposure apparatus is significantly increased (16 times in the above case). In addition to this, there is a problem that the substrate processing capacity per unit time in the exposure process, that is, the throughput is significantly reduced.

Therefore, when the circuit pattern 1 of the liquid crystal display has a size of four times the effective field or more, it is necessary to design the reticle 8 in consideration of the number of divisions of the circuit pattern 1. There is a problem that the load on the design of the reticle 8 increases.

The present invention has been made in consideration of the above points, and it is an object of the present invention to propose a circuit pattern dividing method capable of significantly reducing the load on the design of a reticle.

[0017]

In order to solve such a problem, in the present invention, a display section in which a plurality of electrodes are formed corresponding to a plurality of pixels and a display section connected to each electrode of the display section are provided. A circuit pattern dividing method for forming a circuit pattern on a reticle, the circuit pattern including a conductive portion formed so as to surround the conductive pattern. When dividing the circuit pattern into a plurality of regions, a part of the display portion is provided in at least one divided region. And a part of the conducting portion are included.

Therefore, in the present invention, the circuit pattern is divided so that at least one divided area includes a part of the display part and a part of the conductive part.
The number of divisions of the circuit pattern can be greatly reduced.

[0019]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below in detail with reference to the drawings.

In FIG. 1, reference numeral 10 denotes an exposure apparatus according to the embodiment as a whole, and a reticle 11A, 11B, 11C, 11D in which division patterns each of which is formed by dividing a liquid crystal display circuit pattern into a plurality of types are formed in order is predetermined. Of the exposure light, and at the same time, the exposure light is divided into patterns 12A to 11D formed on the reticles 11A to 11D.
The projected images of the divided patterns 12A to 12F obtained by passing through 12B, 12C, 12D, 12E and 12F are not shown in the drawing on the glass substrate 15 placed on the XY stage 14 via the projection optical system 13, respectively. By projecting onto a predetermined position of the resist film, the resist film formed on the glass substrate 15 can be exposed according to the circuit pattern of the liquid crystal display.

In this case, the circuit pattern of the liquid crystal display has a size four times or more the size of the effective field, and one division pattern includes a part of the display part and a part of the peripheral part. It is divided into 6 types. Further, in each of the reticles 11A, 11B, 11C and 11D, one relatively large division pattern is formed in each of the reticles 11A and 11B so that the areas of the surfaces on which the division patterns 12A and 12B are formed can be effectively used. And the reticle 11C and 11D each have two relatively small division patterns 1
2C, 12D and 12E, 12F are formed.

Each of the reticles 11A to 11D is held by a sequential exchange (hereinafter referred to as a reticle engine) 16, and the reticle engine 16 is located above the projection optical system 13 and above the projection optical system 13. It is movably arranged on a two-dimensional plane parallel to the end surface 13A. Further, the reticle engine 16 is driven and controlled by a drive control unit (not shown), and a desired reticle 11A among the reticles 11A to 11D is placed at a predetermined position above the projection optical system 13.
1B, 11C or 11D can be arranged.

One side of the XY stage 14
4A is arranged movably in the X-axis direction (arrow X) and the Y-axis direction (arrow Y) on a two-dimensional plane parallel to the lower end surface of the projection optical system 13 and parallel to the lower end surface of the projection optical system 13. Has been done. Further, at predetermined positions around the XY stage 14, first and second position detectors 17 and 18 which are interferometers or the like for detecting the movement amount of the XY stage 14 in the X-axis direction and the Y-axis direction are arranged. ing. As a result, in the exposure apparatus 10, the drive motor (not shown) is driven while detecting the movement amounts of the XY stage 14 in the X-axis direction and the Y-axis direction by the first and second position detectors 17 and 18. The XY stage 14 is moved to move the glass substrate 15 placed on the one surface 14A of the XY stage 14 to a desired reticle 11A, 11B, 11C or 1D.
The exposure area corresponding to the position can be moved and positioned so as to face the lower end surface of the projection optical system 13.

In practice, in the exposure apparatus 10, first, the reticle engine 16 is moved to move the reticle 1 for example.
1A is arranged at a predetermined position above the projection optical system 13, and the XY stage 14 is moved so that the exposure area corresponding to the reticle 11A of the resist film on the glass substrate 15 faces the lower end surface of the projection optical system 13. Position. In this state, the reticle 11A is irradiated with exposure light emitted from an illumination optical system (not shown) arranged above the projection optical system 13, and the projection image obtained by the exposure light passing through the division pattern 12A of the reticle 11A. Projection optical system 13
By projecting on the resist film on the glass substrate 15 via the, the resist film on the glass substrate 15 is exposed according to the division pattern 12A.

Further, in the exposure apparatus 10, the reticle 11 described above is also used in the other reticles 11B to 11D.
The resist film on the glass substrate 15 is exposed in the same manner as in the case A, and thus the resist film on the glass substrate 15 is exposed according to the circuit pattern of the liquid crystal display. However, in this exposure apparatus 10, when the resist film on the glass substrate 15 has, for example, two or more exposure regions corresponding to the divided pattern 12A of the reticle 11A, the reticle 11A is fixed after the first exposure. Then, the glass substrate 15
Only this is moved, and the second exposure is performed from this.

Further, in this exposure apparatus 10, the division pattern 12C is exposed using the reticle 11 in which two division patterns 12C and 12D (or division patterns 12E and 12F) are formed like the reticle 11C (or reticle 11D). In this case, only the divided pattern 12C is irradiated with the exposure light by using a light shielding band (not shown). Prior to the irradiation of the exposure light, the reticle charger 16 is moved to make the divided pattern 12C of the reticle 11C face the upper end surface 13A of the projection optical system 13, and the XY stage 14 is moved to move the resist film on the glass substrate 15 The exposure area corresponding to the divided pattern 12C is positioned so as to face the lower end surface of the projection optical system 13.

Thus, the projection image obtained by the exposure light passing through the division pattern 12C is projected on the resist film on the glass substrate 15 through the projection optical system 13, and the resist on the glass substrate 15 is formed according to the division pattern 12C. Expose the film.

Here, in the case where the circuit pattern of such a liquid crystal display has a size four times or more the size of the effective field, a method of dividing the circuit pattern will be described below. First, in the liquid crystal display circuit pattern, the size of the display portion is determined based on the number of pixels (electrodes) of red, green, and blue and the size of each pixel (electrode) of red, green, and blue. . However, the electrodes formed on the display section are relatively small in size and arranged regularly, so that the display section can be freely divided. Further, in the peripheral portion, the number of lead wire groups is determined based on the number of red, green, and blue pixels of the display unit.

In this case, in the peripheral portion, first, the number of lead wire groups provided at the first and second end portions is the number of red, green, and blue pixels in the longitudinal direction of the display portion, and Based on the corresponding lead wire set unit (eg 192 or 240)

[Equation 1] It is represented by Also, in this peripheral part, the third and fourth
Based on the number of red, green, and blue pixels in the direction orthogonal to the longitudinal direction of the display unit and the unit of assembly of the lead wires corresponding to each pixel, Formula (2)

[Equation 2] It is represented by

By the way, each lead wire group at each of the first, second and third end portions of the peripheral portion has substantially the same pattern. Therefore, in order to divide the peripheral portion, for example, the first end portion, the peripheral portion is divided at the boundary between the adjacent lead wire groups. In this case, for example, one lead wire group is formed on the reticle 11 and the reticle 11
Is used in the exposure apparatus 10,
In the above, the glass substrate 15 is repeatedly exposed according to the number of lead wires provided at the first end of the peripheral portion, and the resist on the glass substrate 15 is exposed according to the first end of the peripheral portion. The film can be exposed.

However, when a relatively large number of lead wire groups are provided at the first end portion of the peripheral portion, the number of exposure processes corresponding to the first single portion of the peripheral portion in the exposure apparatus 10 depends on the number of lead wires. Relatively large depending on the number of groups. That is, when, for example, eight lead wire groups are provided at the first end portion in the peripheral portion, the exposure process is repeated eight times only at this first end portion. For this reason, in order to divide the first end portion of the peripheral portion, the adjacent lead wire groups are used as boundaries, and for example, two to three lead wire groups are divided into one division pattern according to the effective field. To do. This makes it possible to reduce the number of divisions when dividing the first end portion of the peripheral portion, and form the two or three lead wire groups of the first end portion thus divided on the reticle 11, and the reticle 11 concerned. When the exposure process is performed by using, the number of times of the exposure process can be reduced.

In addition to the method of dividing the peripheral portion described above, when dividing the circuit pattern of the liquid crystal display, the peripheral portion and the display portion are not separated, and one portion of the display portion and the peripheral portion are combined into one division pattern. It is divided so as to include a part (that is, a peripheral portion having two to three lead wire groups).
Thereby, the number of divisions of the liquid crystal display circuit pattern can be reduced.

In practice, as a circuit pattern of a liquid crystal display having a size four times or more the size of the effective field, 1024 red, green, and blue pixels are provided in the display section along the longitudinal direction, respectively, and A circuit pattern in which 768 pixels are provided along the direction orthogonal to the longitudinal direction will be specifically described. As shown in FIG. 2A, in this circuit pattern 20, each of the first and second end portions 21A and 21B of the peripheral portion 21 has eight lead wire groups 22 (equation (1) described above). However, the third end portion 21C of the peripheral portion 21 has four lead wire groups 23 (equation (2) described above). The set unit of lead wire is 192.

In this case, in the liquid crystal display circuit pattern 20, the size of the circuit pattern 20
(Or second) and third end portions 21A (or 21B) and 21C are divided based on the number of lead wire groups 22 and 23 and the effective field, respectively. First, circuit pattern 2
The first end portion 21A and the second end portion 21B of the peripheral portion 21 divide the two lead wire groups 22 into two along one direction 0 along the direction orthogonal to the longitudinal direction. Further, each block formed by dividing the circuit pattern 20 into two is configured such that the first end portion 21A and the second end portion 21B form the three lead wire groups 22 into one pattern on the center side of the circuit pattern 20. Divide into two. In this way, the circuit pattern 20 is divided into four along the direction orthogonal to the longitudinal direction.

Next, the circuit pattern 20 is divided along the longitudinal direction so that the third end portion 21C forms the two lead wire groups 23 into one pattern. This allows circuit pattern 2
0 is divided into eight division patterns 12A to 12F. As described above, in the above-described division method, the display portion 24 has a length corresponding to three or less lead wire groups 22 along the longitudinal direction, and 2 along the direction orthogonal to the longitudinal direction.
The display section 24 and the peripheral section 21 having a length corresponding to one lead wire group 23 and contacting the display section 24 along the longitudinal direction and / or the direction orthogonal to the longitudinal direction are divided into one division pattern. . As a result, in this embodiment, the number of divisions can be halved as compared with the conventional case where the circuit pattern 1 (FIG. 7) having a size four times as large as the effective field or more is divided into 16 division patterns HR. Has been done.

The two divided patterns 12A on the side of the first end 21A divided from the central portion of the circuit pattern 20 in this manner are in contact with the number of the lead wire groups 22. The direction in which it is present and the size of the display unit 24 are substantially the same, and the patterns are substantially the same as a whole.
Further, the two division patterns 12B on the second end 21B side are also substantially the same pattern for the same reason as the case of the division pattern 12A described above. Therefore, as shown in FIG. 2B, when the above-described division patterns 12A to 12F are formed on the reticle, the division patterns 12A and 12B are formed on the reticles 11A and 11B, respectively, and the division patterns 12C and 12C are formed. 12D and division patterns 12E and 12F, respectively, for reticles 11C and 11C, respectively.
Form D. As a result, in each of the reticles 11A to 11D, the area of the surface on which the divided patterns 12A to 12F are formed can be effectively used.

In the above configuration, the circuit pattern 20 of the liquid crystal display is connected to the size of the circuit pattern 20, the lead wire group 22 of the first (or second) and third end portions 21A (or 21B) and 21C, respectively. Based on the number of 23 and the effective field, the display portion 24 has a length corresponding to three or less lead wire groups 22 along the longitudinal direction, and two lead wires along the direction orthogonal to the longitudinal direction. By having the length corresponding to the group 23 and dividing the display unit 24 and the peripheral portion 21 in contact with the display unit 24 as one pattern, the number of divisions of the circuit pattern 20 can be significantly reduced. .

As a result, in the exposure apparatus 10, the circuit pattern 20 of the liquid crystal display has an effective field of 4
When the size is more than twice, the circuit pattern 20 is divided as described above and the divided patterns 12A to 12A-1.
By using the reticles 11A to 11D each having 2F formed therein, the exposure for the circuit pattern 20 is performed as compared with the exposure process (16 times) for the conventional circuit pattern 1 (FIG. 7) having a size four times or more the effective field. The number of treatments can be greatly reduced to 8 times. Thus, the throughput in the exposure process can be greatly improved.

According to the above configuration, the circuit pattern 20 of the liquid crystal display is replaced by the size of the circuit pattern 20,
First (or second) and third ends 21A (or 21B)
, And 21C, respectively, based on the number and effective fields of the lead wire groups 22 and 23, one division pattern 12A to
By dividing so as to include a part of the display section 24 and a part of the peripheral section 21 in 12F, the number of divisions of the circuit pattern 20 of the liquid crystal display can be greatly reduced, and thus the reticle It is possible to realize a circuit pattern division method that can significantly reduce the load on the design.

In the embodiment described above, the circuit pattern 20 of the liquid crystal display is connected to the size of the circuit pattern 20 and leads of the first (or second) and third end portions 21A (or 21B) and 21C, respectively. Based on the number of line groups 22 and the effective field, the display section 24 has a length corresponding to three or less lead wire groups 22 along the longitudinal direction and two leads along the direction orthogonal to the longitudinal direction. The case has been described in which the display section 24 and the peripheral section 21 in contact with the line section 22 are divided into one pattern having a length corresponding to the line group 22, but the present invention is not limited to this, and the liquid crystal display is not limited to this. Of the lead wire groups 22 and 23 of the first (or second) and third end portions 21A (or 21B) and 21C, respectively. And the display section 24 has a length corresponding to at least one lead wire group 22 along the longitudinal direction and the direction orthogonal to the longitudinal direction, if the display section 24 is divided based on the effective field. You may make it divide | segment the peripheral part 21 which touches this and this as one division pattern.

[0041]

As described above, according to the present invention, the circuit pattern is divided so that at least one divided area includes a part of the display part and a part of the conductive part, and thus the circuit pattern is divided. It is possible to significantly reduce the number of pattern divisions, and thus to realize a circuit pattern division method that can significantly reduce the load on the reticle design.

[Brief description of drawings]

FIG. 1 is a schematic perspective view showing a configuration of an exposure apparatus according to an embodiment of the present invention.

FIG. 2 is a schematic plan view for explaining division of a circuit pattern of a liquid crystal display according to an embodiment of the present invention.

FIG. 3 is a schematic plan view showing a configuration of a circuit pattern of a liquid crystal display.

FIG. 4 is a schematic plan view for explaining the case where the size of the circuit pattern of the liquid crystal display is smaller than the size of the effective field.

FIG. 5 is a schematic plane view for explaining division of the circuit pattern of the liquid crystal display when the circuit pattern is equal to or larger than the effective field size and has a size up to about twice the effective field size. It is a figure.

FIG. 6 is a schematic for explaining division of a circuit pattern of a liquid crystal display when the circuit pattern has a size that is twice or more the size of an effective field and up to about 4 times the size of the effective field. It is a linear plan view.

FIG. 7 is a schematic plan view for explaining division when a circuit pattern of a conventional liquid crystal display has a size four times or more the size of an effective field.

[Explanation of symbols]

1, 20 ... Circuit pattern, 2, 24 ... Display section, 3,
21 ... peripheral part, 4,22 ... lead wire group 5,6,
7, 8, 11 ... Reticle, 10 ... Exposure device, 13 ...
... Projection optical system, 15 ... Glass substrate, 12A, 12B,
12C, 12D, 12E, 12F ... Division pattern.

Claims (2)

[Claims] 1. A circuit comprising a display section in which a plurality of electrodes are formed corresponding to a plurality of pixels, and a conductive section which is electrically connected to each of the electrodes of the display section and surrounds the display section. A circuit pattern dividing method for forming a pattern on a reticle, wherein when the circuit pattern is divided into a plurality of regions, at least one divided region includes a part of the display part and a part of the conductive part. A method for dividing a circuit pattern, characterized in that 2. The circuit pattern is exposed on a photosensitive substrate by an exposure device having a projection optical system, and the circuit pattern has a size of the circuit pattern, the number of conductive portions, and the projection optical system. 2. The circuit pattern dividing method according to claim 1, wherein the division is performed based on at least one of the effective diameter and the effective diameter.