Semiconductor device

1. A semiconductor device, comprising:

a substrate;

an electrode structure on the substrate, the electrode structure including electrodes stacked on the substrate, the electrodes extending parallel to a first direction; and

a plurality of vertical patterns passing through the electrode structure,

the vertical patterns including first vertical patterns arranged in the first direction, second vertical patterns arranged in the first direction, and third vertical patterns arranged in the first direction,

the second vertical patterns being adjacent to the first vertical patterns and spaced apart from the first vertical patterns in a second direction crossing the first direction,

the third vertical patterns being adjacent to the second vertical patterns and spaced apart from the second vertical patterns in the second direction,

the first and second vertical patterns being arranged so centers of three most adjacent vertical patterns among the first and second vertical patterns are positioned at vertices of a regular triangle, and

the second and third vertical patterns being arranged so centers of three most adjacent vertical patters among the second and third vertical patterns are positioned at vertices of a scalene triangle;

a plurality of bit lines connected to the plurality of vertical patterns; and

a plurality of subsidiary lines between the plurality of vertical patterns and the plurality of bit lines in a third direction vertical to a top surface of the substrate, each of the plurality of subsidiary lines connecting a corresponding one of the plurality of bit lines to at least two of the plurality of vertical patterns that are spaced apart from each other in the second direction, wherein

the vertical patterns further include fourth vertical patterns arranged in the first direction,

the fourth vertical patterns are adjacent to the third vertical patterns,

the fourth vertical patterns are spaced apart from the third vertical patterns in the second direction,

the third and the fourth vertical patterns are arranged so centers of three most adjacent vertical patterns among the third and the fourth vertical patterns are positioned at vertices of a second regular triangle,

the first vertical patterns are adjacent to an edge of the electrode structure,

the vertical patterns further include dummy vertical patterns arranged in the first direction,

the dummy vertical patterns are adjacent to the fourth vertical patterns,

the dummy vertical patterns are spaced apart from the fourth vertical patterns in the second direction,

the vertical patterns further include fifth vertical patterns, sixth vertical patterns, seventh vertical patterns, and eighth vertical patterns that are symmetrically arranged about the dummy vertical patterns with respect to the first vertical patterns, second vertical patterns, third vertical patterns, and fourth vertical patterns, respectively,

the plurality of subsidiary lines include first subsidiary lines and second subsidiary lines,

the first subsidiary lines connect the third vertical patterns to the sixth vertical patterns, respectively,

the second subsidiary lines connect the fourth vertical patterns to the fifth vertical patterns, respectively, and

the first subsidiary lines and the second subsidiary lines have a bar-shaped structure extending in the second direction.

2. The semiconductor device of claim 1 , wherein the first subsidiary lines overlap the dummy vertical patterns, respectively, when viewed in a plan view.

3. The semiconductor device of claim 1 , wherein the first subsidiary lines and the second subsidiary lines are alternatingly arranged in the first direction, and

lengths of the first subsidiary lines in the second direction are different from lengths of the second subsidiary lines in the second direction.

4. The semiconductor device of claim 1 , further comprising:

an additional electrode structure spaced apart from the electrode structure in a direction opposite to the second direction, wherein

the plurality of subsidiary lines include third subsidiary lines,

the additional electrode structure includes substantially a same configuration as the electrode structure,

the third subsidiary lines connect the eighth vertical patterns of the additional electrode structure to the first vertical patterns of the electrode structure, respectively, and

the third subsidiary lines include a bar-shaped structure extending in the second direction.

5. The semiconductor device of claim 4 , wherein

the plurality of subsidiary lines include fourth subsidiary lines connecting seventh vertical patterns of the additional electrode structure to the second vertical patterns of the electrode structure, respectively, and

the fourth subsidiary lines include a bar-shaped structure extending in the second direction.

6. The semiconductor device of claim 5 , wherein

the plurality of bit lines include first, second, third, and fourth bit lines that are connected to the first, second, third, and fourth subsidiary lines, respectively, and

the first, second, third, and fourth bit lines extend in the second direction.

7. A semiconductor device, comprising:

a substrate;

an electrode structure on the substrate;

vertical patterns arranged in rows on the substrate,

the vertical patterns extending through the electrode structure in a direction perpendicular to a top surface of the substrate,

the vertical patterns in a same one of the rows being spaced apart from each other in a first direction,

the vertical patterns including first vertical patterns in a first row, second vertical patterns in a second row, and third vertical patterns in a third row,

the first to third rows of vertical patterns being arranged sequentially in a second direction from a same edge of the electrode structure such that the first to third vertical patterns all extend through a first half of the electrode structure along the second direction in a plan view,

each center of two adjacent first vertical patterns being spaced apart from a center of an adjacent second vertical pattern by a diagonal distance that is the same as a distance in the first direction that the centers of the two adjacent first vertical patterns are spaced apart from each other,

the vertical patterns including a dummy row of vertical patterns extending through the electrode structure, and

the third vertical patterns being spaced apart in the second direction from corresponding dummy vertical patterns in the dummy row of vertical patterns;

a plurality of bit lines connected to the vertical patterns; and

a plurality of subsidiary lines between the vertical patterns and the plurality of bit lines in a third direction vertical to a top surface of the substrate, each of the plurality of subsidiary lines connecting a corresponding one of the plurality of bit lines to at least two of the plurality of vertical patterns that are spaced apart from each other in the second direction,

wherein the plurality of subsidiary lines include first subsidiary lines and second subsidiary lines which are alternatingly arranged in the first direction, and

lengths of the first subsidiary lines in the second direction are different from lengths of the second subsidiary lines in the second direction.

8. The semiconductor device of claim 7 , wherein

the vertical patterns further include fourth vertical patterns in a fourth row, fifth vertical patterns in a fifth row, sixth vertical patterns in a sixth row, seventh vertical patterns in a seventh row, and eighth vertical patterns in an eighth row,

the fourth row of vertical patterns is between the dummy row of vertical patterns and the third row of vertical patterns,

the fifth to eighth rows of vertical patterns are arranged sequentially in the second direction from the dummy row of vertical patterns such that the fifth to eighth rows of vertical patterns all extend through a second half of the electrode structure along the second direction in the plan view.

9. The semiconductor device of claim 8 , wherein

the fifth vertical patterns, sixth vertical patterns, seventh vertical patterns, and eighth vertical patterns are symmetrically arranged about the dummy vertical patterns with respect to the first vertical patterns, second vertical patterns, third vertical patterns, and fourth vertical patterns, respectively, and

each center of two adjacent third vertical patterns are spaced apart from a center of a nearby second vertical pattern by a diagonal distance that is different than a distance in the first direction that the centers of the two adjacent third vertical patterns are spaced apart from each other.

10. The semiconductor device of claim 8 , wherein

the fifth vertical patterns, sixth vertical patterns, seventh vertical patterns, and eighth vertical patterns are symmetrically arranged about the dummy vertical patterns with respect to the first vertical patterns, second vertical patterns, third vertical patterns, and fourth vertical patterns, respectively, and

each center of two adjacent third vertical patterns are spaced apart from a center of a nearby second vertical pattern by a diagonal distance that is equal to a distance in the first direction that the centers of the two adjacent third vertical patterns are spaced apart from each other.

11. The semiconductor device of claim 8 , further comprising:

another electrode structure spaced apart from the electrode structure in the second direction, wherein

the electrode structure is a first electrode structure and the other electrode structure is a second electrode structure,

the vertical patterns include additional vertical patterns that extend through the second electrode structure with the same arrangement as the vertical patterns that extend through the first electrode structure such that the vertical patterns include first to eighth vertical patterns and dummy vertical patterns extending through the second electrode structure,

the subsidiary lines further include third subsidiary lines, and fourth subsidiary lines,

the first subsidiary lines connect the third vertical patterns extending through the first electrode structure to corresponding sixth vertical patterns extending through the first electrode structure and spaced apart in the second direction,

the second subsidiary lines connect the fourth vertical patterns extending through the first electrode structure to corresponding fifth vertical patterns extending through the first electrode structure and spaced apart in the second direction,

the first and second subsidiary lines cross over the dummy vertical patterns,

the third subsidiary lines each connect one of the first vertical patterns extending through the first electrode structure to a corresponding one of the eighth vertical patterns extending through the second electrode structure and spaced apart in the second direction, and

the fourth subsidiary lines each connect one of the second vertical patterns extending though the first electrode structure to a corresponding one of the seventh vertical patterns extending through the second electrode structure and spaced apart in the second direction.