Pattern writing and forming method

1. A pattern writing apparatus for radiating an energy beam on a resist that is applied to a target to write patterns thereon comprising:

a memory configured to store pattern data for writing the patterns, the pattern data including a reference radiation amount D 0 for radiating the energy beam, a distribution of a pattern dependency of a pattern-size variation Δ due to a loading effect, and an energy distribution “s” applied to the resist by the energy beam;

a first calculator configured to divide writing regions of the target into grids to provide sub-writing regions in the grids and configured to obtain a distribution of a pattern-area density per sub-writing region based on the pattern data;

a second calculator configured to calculate a radiation amount DC f (x) for correcting a long-range fogging exposure in each sub-writing region based on the pattern-area density and the reference radiation amount D 0 ;

a third calculator configured to calculate a radiation amount DC p (x) for correcting a proximity effect applied to those of the patterns in each sub-writing region based on the pattern data and the reference radiation amount D 0 ;

a fourth calculator configured to calculate a radiation amount D(x) based on the radiation amount DC f (x) the radiation amount DC p (x), the distribution of a pattern dependency, and the energy distribution “s”;

a deciding portion configured to decide radiation locations and a radiation shape of the energy beam based on data on a pattern location and a pattern shape for each of the patterns in the sub-writing regions; and

a radiating portion configured to radiate the energy beam on the radiation location on the target with the radiation shape for a period in which a radiated energy level from the energy beam reaches the radiation amount D(x).

2. The pattern writing apparatus according to claim 1 further comprising:

a proximity-effect processor configured to obtain a distribution of a pattern-size variation Δ(x) per sub-writing region based on the distribution of the pattern-area density and the distribution of the pattern dependency of the pattern-size variation Δ due to the loading effect,

wherein the radiation amount DC f (x) is calculated based on the distribution of the pattern-area density, the reference radiation amount D 0 and the distribution of the pattern-size variation Δ(x), and

wherein the radiation amount DC p (x) is calculated based on the data on the pattern location and the pattern shape in the sub-writing regions, the reference radiation amount D 0 , the distribution of the pattern-size variation Δ(x), and the energy distribution “s” of the energy beam.

3. The pattern writing apparatus according to claim 1 , wherein the radiation amount D(x) includes generating a product of the radiation amount DC f (x) and the radiation amount DC p (x).

4. The pattern writing apparatus according to claim 3 , wherein the fourth calculator uses the radiation amount DC f (x) set to the reference radiation amount D 0 for the calculation of the radiation amount D(x).

5. The pattern writing apparatus according to claim 1 , wherein the fourth calculator uses an equation D(x)=DC p (x)×DC f (x)/(1+(2s(Δ)−1)×(DC p (x)×DC f (x)/C 0 )) for the calculation of the radiation amount D(x).

6. The pattern writing apparatus according to claim 5 , wherein the pattern-size variation Δ involves a non-uniform etching in addition to the loading effect.

7. The pattern writing apparatus according to claim 5 , wherein the fourth calculator uses the radiation amount DC f (x) set to the reference radiation amount D 0 for the calculation of the radiation amount D(x).

8. A pattern forming apparatus comprising:

a memory configured to store pattern data for writing patterns, the pattern data including a reference radiation amount D 0 for radiating an energy beam on a resist-applied target, a distribution of a pattern dependency of a pattern-size variation Δ due to a loading effect, and an energy distribution “s” applied to the resist by the energy beam;

a first calculator configured to divide writing regions of the target into grids to provide sub-writing regions in the grids and configured to obtain a distribution of a pattern-area density per sub-writing region based on the pattern data;

a second calculator configured to calculate a radiation amount DC f (x) for correcting a long-range fogging exposure in each sub-writing region based on the pattern-area density and the reference radiation amount D 0 ;

a third calculator configured to calculate a radiation amount DC p (x) for correcting a proximity effect applied to those of the patterns in each sub-writing region based on the pattern data and the reference radiation amount D 0 ;

a fourth calculator configured to calculate a radiation amount D(x) based on the radiation amount DC f (x) the radiation amount DC p (x), the distribution of a pattern dependency, and the energy distribution “s”;

a deciding portion configured to decide radiation locations and radiation shapes of the energy beam based on data on pattern locations and pattern shapes of the patterns in the sub-writing regions and radiating the energy beam on the radiation locations on the target with the radiation shapes for a period in which a radiated energy level from the energy beam reaches the radiation amount D(x), thus writing the patterns on the resist;

a developing portion configured to develop the pattern-written resist to form a resist pattern; and

an etching portion configured to etch the target with the resist pattern as a mask to form the patterns on the target.

9. The pattern forming apparatus according to claim 8 further comprising:

a proximity-effect processor configured to obtain a distribution of pattern-size variation Δ(x) per sub-writing region based on the distribution of the pattern-area density and the distribution of the pattern dependency of pattern-size variation Δ due to the loading effect,

wherein the radiation amount DC f (x) is calculated based on the distribution of the pattern-area density, the reference radiation amount D 0 and the distribution of the pattern-size variation Δ(x), and

wherein the radiation amount DC p (x) is calculated based on the data on the pattern locations and the pattern shapes in the sub-writing regions, the reference radiation amount D 0 , the distribution of the pattern-size variation Δ(x), and the energy distribution “s” of the energy beam.

10. The pattern forming apparatus according to claim 8 , wherein the radiation amount D(x) includes generating a product of the radiation amount DC f (x) and the radiation amount DC p (x).

11. The pattern forming apparatus according to claim 10 , wherein the fourth calculator uses the radiation amount DC f (x) set to the reference radiation amount D 0 for the calculation of the radiation amount D(x).

12. The pattern forming apparatus according to claim 8 , wherein the fourth calculator uses an equation D(x)=DC p (x)×DC f (x)/(1+(2s(Δ)−1)×(DC p (x)×DC f (x)/C 0 )) for the calculation of the radiation amount D(x).

13. The pattern forming apparatus according to claim 12 , wherein the pattern-size variation Δ involves a non-uniform etching addition to the loading effect.

14. The pattern forming apparatus according to claim 12 , wherein the fourth calculator uses the radiation amount DC f (x) set to the reference radiation amount D 0 for the calculation of the radiation amount D(x).