Mask and pattern forming method

1. A mask comprising:

a substrate including a first surface, the substrate being light transmissive;

a first pattern portion including a plurality of first optical members provided on the first surface and arranged periodically in a first direction along the first surface, a light transmittance of the first optical members being lower than a light transmittance of the substrate, a distance between the adjacent two first optical members being a first distance; and

a second pattern portion including a plurality of second optical members provided on the first surface and arranged periodically in the first direction, a light transmittance of the second optical members being lower than the light transmittance of the substrate, a distance between the adjacent two second optical members being a second distance different from the first distance, the second pattern portion including a first member, the first member being light transmissive, and at least a portion of the first member being provided between the second optical members.

2. The mask according to claim 1 , wherein

when a thickness of the first member is taken as d 1 (nanometer), a refractive index of the first member is taken as n 1 , a wavelength of the first light is taken as A (nanometer), and a phase difference between a first phase of a light penetrating the first pattern portion after a first light being incident on the first pattern portion and a second phase of a light penetrating the second pattern portion after the first light being incident on the second pattern portion is taken as ph (degree), the d 1 is not less than 0.8 times and not more than 1.2 times of ph·λ/{360(n 1 −1)}.

3. The mask according to claim 2 wherein

the phase difference is not less than 45 degrees and not more than 180 degrees.

4. The mask according to claim 1 wherein

the first member includes a silicon oxide.

5. The mask according to claim 1 wherein

when an angle between the first light and the first surface is 90 degrees,

a distance between centers of the adjacent two second optical members in the first direction is p 2 (nanometer),

a wavelength of the first light is λ (nanometer),

a numerical number of a projection optical system is NA 1 , and a numerical aperture of an illumination optical system is NA 2 ,

the p 2 is smaller than λ/[{1+(NA 2 /NA 1 )}NA 1 ].

6. The mask according to claim 1 wherein

when the first light is slanted to the first surface,

a second light symmetric to the first light around a first axis perpendicular to the first surface is incident to the first pattern portion and the second pattern portion,

a distance between centers of the adjacent two second optical members in the first direction is p 2 (nanometer),

a wavelength of the first light and the second light is λ (nanometer),

a numerical number of a projection optical system is NA 1 , a numerical aperture of an illumination optical system is NA 2 , and an offset of the numerical aperture of the illumination optical system is NA off ,

the p 2 is smaller than λ/[{1+(NA 2 /NA 1 )+(NA off /NA 1 )}NA 1 ].

7. The mask according to claim 1 wherein

a first ratio of the first distance to a third distance between centers of the adjacent two first optical members in the first direction is different from a second ratio of the second distance to a fourth distance between centers of the adjacent two second optical members in the first direction.

8. The mask according to claim 7 wherein

the third distance is equal to the fourth distance.

9. A mask comprising:

a substrate including a first surface, the substrate being light transmissive;

a first pattern portion including a plurality of first optical members provided on the first surface and arranged periodically in a first direction along the first surface, a light transmittance of the first optical members being lower than a light transmittance of the substrate, a distance between the adjacent two first optical members being a first distance; and

a second pattern portion including a plurality of second optical members provided on the first surface and arranged periodically in the first direction, a light transmittance of the second optical members being lower than the light transmittance of the substrate, a distance between the adjacent two second optical members being a second distance different from the first distance, the second pattern portion including a groove portion provided on the substrate, and a position of the groove portion in the first direction being between the adjacent two second optical members.

10. The mask according to claim 9 , wherein

when a depth of the groove portion is taken as d 2 (nanometer), a refractive index of the substrate is taken as n 2 , a wavelength of the first light is taken as λ (nanometer), and a phase difference between the first phase and the second phase is taken as ph (degree), the d 2 is not less than 0.8 times and not more than 1.2 times of ph˜λ/{360(n 2 −1)}.

11. The mask according to claim 10 wherein

the phase difference is not less than 45 degrees and not more than 180 degrees.

12. The mask according to claim 9 wherein

a first ratio of the first distance to a third distance between centers of the adjacent two first optical members in the first direction is different from a second ratio of the second distance to a fourth distance between centers of the adjacent two second optical members in the first direction.

13. The mask according to claim 12 wherein

the third distance is equal to the fourth distance.

14. A pattern forming method, comprising:

the method being based on a mask including:

a substrate including a first surface, the substrate being light transmissive;

a first pattern portion including a plurality of first optical members provided on the first surface and arranged periodically in a first direction along the first surface, a light transmittance of the first optical members being lower than a light transmittance of the substrate, a distance between the adjacent two first optical members being a first distance; and

a second pattern portion including a plurality of second optical members provided on the first surface and arranged periodically in the first direction, a light transmittance of the second optical members being lower than the light transmittance of the substrate, a distance between the adjacent two second optical members being a second distance different from the first distance,

disposing the mask and a semiconductor wafer;

causing a first light from an illumination optical system to enter the first pattern portion and the second pattern portion;

causing a first phase of a light penetrating the first pattern portion to be different from a second phase of a light penetrating the second portion by the mask, and emitting a 0-order diffraction light, a +1-order diffraction light and a −1-order diffraction light of respective optical images of the light of the first phase and the light of the second phase to a projection optical system;

causing the 0-order diffraction light to penetrate by the projection optical system; and

forming a pattern on the semiconductor wafer by the semiconductor wafer being irradiated with the 0-order diffraction light.

15. The method according to claim 14 , wherein

the second pattern portion includes a first member, the first member being light transmissive, and

at least a portion of the first member being provided between the second optical members.

16. The method according to claim 15 , wherein

when a thickness of the first member is taken as d 1 (nanometer), a refractive index of the first member is taken as n 1 , a wavelength of the first light is taken as λ (nanometer), and a phase difference between the first phase and the second phase is taken as ph (degree), the d 1 is not less than 0.8 times and not more than 1.2 times of ph·A/{360(n 1 −1)}.

17. The method according to claim 14 , wherein

the second pattern portion includes a groove portion provided on the substrate, and

a position of the groove portion in the first direction is between the adjacent two second optical members.

18. The method according to claim 17 , wherein

when a depth of the groove portion is taken as d 2 (nanometer), a refractive index of the substrate is taken as n 2 , a wavelength of the first light is taken as λ (nanometer), and a phase difference between the first phase and the second phase is taken as ph (degree), the d 2 is not less than 0.8 times and not more than 1.2 times of ph·λ/{360(n 2 −1)}.

19. The method according to claim 14 , wherein

when an angle between the first light and the first surface is 90 degrees,

a distance between centers of the adjacent two second optical members in the first direction is p 2 (nanometer),

a wavelength of the first light is λ (nanometer),

a numerical number of a projection optical system is NA 1 , and a numerical aperture of an illumination optical system is NA 2 ,

the p 2 is smaller than λ/[{1+(NA 2 /NA 1 )}NA 1 ].

20. The method according to claim 14 , wherein

when the first light is slanted to the first surface,

a second light symmetric to the first light around a first axis perpendicular to the first surface is incident to the first pattern portion and the second pattern portion,

a distance between centers of the adjacent two second optical members in the first direction is p 2 (nanometer),

a wavelength of the first light and the second light is λ (nanometer),

a numerical number of a projection optical system is NA 1 , a numerical aperture of an illumination optical system is NA 2 , and an offset of the numerical aperture of the illumination optical system is NA off ,

the p 2 is smaller than λ/[{1+(NA 2 /NA 1 )+(NA off /NA 1 )}NA 1 ].