Glass substrate for mask blank, mask blank, photomask, and method for manufacturing glass substrate for mask blank
A glass substrate for a mask blank includes a rectangular-shaped main surface on which a film having a circuit pattern is to be formed. The main surface includes a quadrangular peripheral frame and a square-shaped center area defined by excluding the frame. The center area has a longitudinal length of 142 mm and a lateral length of 142 mm. A surface morphology of the center area is expressed by { z ( x , y ) = ∑ k = 0 N 1 ∑ l = 0 N 2 a kl P k ( x ) P l ( y ) P k ( x ) = 1 2 k k ! d k dx k [ ( x 2 - 1 ) k ] P l ( y ) = 1 2 l l ! d l dy l [ ( y 2 - 1 ) l ] . A flatness of a sum of compositing all of a kl P k (x)P l (y) is less than or equal to 20 nm when a sum of k and l is greater than or equal to 3 and less than or equal to 9. The flatness is less than or equal to 20 nm when a sum of k and l is greater than or equal to 10 and less than or equal to 30.
1. A glass substrate for a mask blank, the glass substrate comprising:
a rectangular-shaped main surface on which a film having a circuit pattern is to be formed;
wherein the rectangular-shaped main surface includes a quadrangular peripheral frame and a square-shaped center area defined by excluding the quadrangular peripheral frame from the rectangular-shaped main surface,
wherein the square-shaped center area has a longitudinal length of 142 mm and a lateral length of 142 mm,
wherein a surface morphology of the square-shaped center area z (x, y) is expressed by
{
z
(
x
,
y
)
=
∑
k
=
0
N
1
∑
l
=
0
N
2
a
kl
P
k
(
x
)
P
l
(
y
)
P
k
(
x
)
=
1
2
k
k
!
d
k
dx
k
[
(
x
2
-
1
)
k
]
P
l
(
y
)
=
1
2
l
l
!
d
l
dy
l
[
(
y
2
-
1
)
l
]
wherein x indicates a coordinate in a lateral direction of the mask blank, y indicates a coordinate in a longitudinal direction of the mask blank, and z indicates a coordinates in a height direction of the mask blank, and k and l are each zero or a natural number,
wherein a flatness of a sum of compositing all of a kl P k (x)P l (y) is less than or equal to 20 nm in a case where a sum of k and l is greater than or equal to 3 and less than or equal to 9, and
wherein the flatness of the sum of compositing all of a kl P k (x)P l (y) is less than or equal to 20 nm in a case where a sum of k and l is greater than or equal to 10 and less than or equal to 30.
2. A mask blank comprising:
the glass substrate of claim 1 ; and
the film on which the circuit pattern is to be formed.
3. The mask blank as claimed in claim 2 , wherein the film is a light-shielding film that shields light.
4. The mask blank as claimed in claim 2 ,
wherein the film is an absorbing film that absorbs light, and
wherein a reflection film that reflects the light is provided between the absorbing film and the glass substrate.
5. A photomask comprising:
the glass substrate of claim 1 ; and
the film having the circuit pattern.
6. The photomask as claimed in claim 5 , wherein the film is a light-shielding film that shields light.
7. The photomask as claimed in claim 5 ,
wherein the film is an absorbing film that absorbs light, and
wherein a reflection film that reflects the light is provided between the absorbing film and the glass substrate.
8. A method for manufacturing the glass substrate of claim 1 , the method comprising:
supplying a polishing slurry between the glass substrate and a polishing pad;
polishing an entire area of the main surface of the glass substrate; and
processing a local area of the main surface of the glass substrate after the polishing;
wherein the polishing pad includes a porous resin layer that contacts the main surface of the glass substrate, and
wherein a resin included in the porous resin layer has a 100% modulus that is greater than or equal to 5 MPa and less than or equal to 14 MPa.
9. A mask blank comprising:
a glass substrate including a rectangular-shaped main surface; and
a film formed on the rectangular-shaped main surface of the glass substrate, and a circuit pattern is to be formed on the film;
wherein the main surface of the film on the opposite side of the glass substrate is rectangular-shaped and includes a quadrangular peripheral frame and a square-shaped center area defined by excluding the quadrangular peripheral frame from the rectangular-shaped main surface,
wherein the square-shaped center area has a longitudinal length of 142 mm and a lateral length of 142 mm,
wherein a surface morphology of the square-shaped center area z (x, y) is expressed by
{
z
(
x
,
y
)
=
∑
k
=
0
N
1
∑
l
=
0
N
2
a
kl
P
k
(
x
)
P
l
(
y
)
P
k
(
x
)
=
1
2
k
k
!
d
k
dx
k
[
(
x
2
-
1
)
k
]
P
l
(
y
)
=
1
2
l
l
!
d
l
dy
l
[
(
y
2
-
1
)
l
]
wherein x indicates a coordinate in a lateral direction of the mask blank, y indicates a coordinate in a longitudinal direction of the mask blank, and z indicates a coordinates in a height direction of the mask blank, and k and l are each zero or a natural number,
wherein a flatness of a sum of compositing all of a kl P k (x)P l (y) is less than or equal to 20 nm in a case where a sum of k and l is greater than or equal to 3 and less than or equal to 9, and
wherein the flatness of the sum of compositing all of a kl P k (x)P l (y) is less than or equal to 20 nm in a case where a sum of k and l is greater than or equal to 10 and less than or equal to 30.
10. The mask blank as claimed in claim 9 , wherein the film is a light-shielding film that shields light.
11. The mask blank as claimed in claim 9 ,
wherein the film is an absorbing film that absorbs light, and
wherein a reflection film that reflects the light is provided between the absorbing film and the glass substrate.
12. The mask blank as claimed in claim 9 ,
wherein the film is a low reflection film,
wherein the mask blank further comprises:
a reflection film that reflects light, provided between the glass substrate and the low reflection film; and
an absorbing film that absorbs the light, provided between the reflection film and the low reflection film, and
wherein a low reflection film reflects an inspection light of the circuit pattern to be formed on the absorbing film, with reflectivity lower than the absorbing film.