Self-organization material and pattern formation method
A pattern formation method according to an embodiment includes providing a substrate in which protrusions each having a tapered shape are provided on a main surface. The method further includes supplying the main surface with spherical particles equal in diameter to make the spherical particles arrange in a triangular lattice form such that each of the protrusions is at least partially positioned within a region surrounded by the main surface and three of the spherical particles adjacent to one another.
1. A pattern formation method comprising:
providing a substrate in which protrusions each having a tapered shape are provided on a main surface; and
supplying the main surface with spherical particles equal in diameter to make the spherical particles arrange in a triangular lattice form such that each of the protrusions is at least partially positioned within a region surrounded by the main surface and three of the spherical particles adjacent to one another.
2. The method of claim 1 , wherein each of the spherical particles is a core-shell particle including a core and a shell covering the core.
3. The method of claim 2 , further comprising, after the spherical particles are arranged, removing the protrusions and the shell of each of the spherical particles such that the core of each of the spherical particles remains.
4. The method of claim 3 , further comprising processing the main surface by using the remaining cores as a mask.
5. The method of claim 1 , wherein the protrusions are provided on the main surface in such a manner that each of the protrusions is positioned on any of lattice points of a triangular lattice.
6. The method of claim 1 , wherein two or more of the protrusions are provided on the main surface such that each of them is positioned on any of lattice points of a triangular lattice, and the remainders of the protrusions are provided on the main surface such that each of them is positioned on any of median points of triangles, triangles of a first orientation and triangles of a second orientation opposite to the first orientation being obtained when connecting adjacent lattice points of the triangular lattice by line segments, and the median points of the triangles being median points of the triangles of the first orientation.
7. The method of claim 6 , wherein the protrusions are provided on the main surface with a center-to-center distance d calculated by the following equation (4) or (7):
d
=
(
3
h
+
2
i
)
2
+
(
3
h
+
6
i
+
6
j
-
2
)
2
3
×
r
(
4
)
d
=
2
m
2
+
4
mn
+
4
n
2
3
×
2
r
(
7
)
wherein
in the equation (4), r represents a radius of the spherical particles, and h, i, and j each independently represent an integer, and
in the equation (7), r represents a radius of the spherical particles, m and n each independently represent an integer, and m and n cannot be zero at the same time.
8. The method of claim 7 , wherein the center-to-center distance d is 4r or more.
9. The method of claim 7 , wherein the center-to-center distance d is 20r or less.
10. The method of claim 1 , wherein each of the protrusions is formed to have a pyramidal shape.
11. The method of claim 1 , wherein each of the protrusions is formed to have a circular cone shape.
12. The method of claim 1 , wherein the protrusions are provided on the main surface such that a radius r 1 and a radius r satisfy a relationship of the following equation (9):
r
1
≤
2
r
3
(
9
)
wherein the radius r 1 is a radius of a bottom of each of the protrusions, and the radius r is a radius of each of the spherical particles.
13. The method of claim 1 , wherein the protrusions are provided on the main surface such that a radius r 2 and a radius r satisfy a relationship of the following equation (11):
r
2
≤
2
r
3
-
2
rh
-
h
2
(
11
)
wherein the radius r 2 is a radius of each of the protrusions at a height h, and the radius r is a radius of each of the spherical particles.
14. The method of claim 1 , wherein the protrusions are provided on the main surface such that each has a height lower than a radius r of the spherical particles.
15. The method of claim 1 , wherein the spherical particles have a radius of 10 nm or more.
16. The method of claim 1 , wherein the protrusions are formed by imprinting.
17. A method of manufacturing a stamper, comprising:
forming a protruding pattern or a recessed pattern on a main surface of a substrate by the method of claim 1 ; and
performing electroforming on the main surface having the protruding pattern or the recessed pattern formed thereon, to form a metal layer having a surface shape corresponding to the protruding pattern or the recessed pattern.
18. A method of manufacturing a device, comprising:
forming a protruding pattern or a recessed pattern on a main surface of a substrate by the method of claim 1 ;
forming a resin layer on another substrate; and
transferring the protruding pattern or the recessed pattern onto the resin layer.