Electron beam writing apparatus and position displacement amount correcting method
The present invention provides an electron beam writing apparatus and an image placement error correcting method each capable of calculating a high-accuracy correction amount relative to an image placement error in consideration of a difference in required unit area of height distribution data between the shape of a back surface of an EUV mask and the shape of a surface of a pin chuck. Of back surface shape data of the EUV mask necessary to perform an image placement error correction of each pattern, the back surface shape data of a position brought into contact with each pin of the pin chuck is extracted. The image placement error is calculated only from the extracted back surface shape data.
1. An electron beam writing apparatus that corrects an image displacement error of an EUV mask based on a back surface shape of the EUV mask and a surface shape of an electrostatic pin chuck contacting the back surface of the EUV mask to hold the EUV mask on the electrostatic pin chuck, said electron beam writing apparatus comprising:
a measuring unit that measures flatness of the back surface shape of the EUV mask held on the electrostatic pin chuck;
a first storing unit that stores back surface shape data of the EUV mask measured by the measuring unit;
a second storing unit that stores surface shape data of the electrostatic pin chuck, comprising shape data of pins of the electrostatic pin chuck based on a relationship with center coordinates of the EUV mask, pitch data between the pins, and chucked region data;
a data extraction unit that extracts only a portion of the back surface shape data of the EUV mask using the surface shape data of the electrostatic pin chuck, the extracted portion of the back surface shape data of the EUV mask including only back surface shape data of the EUV mask at positions of the EUV mask that frictionally contact the pins of the electrostatic pin chuck;
a first calculating unit that approximates a shape of the EUV mask by a polynomial expression of only the extracted portion of the back surface shape data of the EUV mask extracted by the data extraction unit;
a tilt calculating unit that determines a local tilt distribution at back surface of the EUV mask from the polynomial expression that approximates the shape of the EUV mask using only the back surface shape data of the EUV mask at the positions of the EUV mask that frictionally contact the pins of the electrostatic chuck;
a second calculating unit that calculates an amount of image displacement error based on the determined local tilt distribution and a predetermined amount of distortion where the back surface of the EUV mask is held by the electrostatic pin chuck when a pattern is written onto a front surface of the EUV mask;
a coefficient calculating unit that obtains a coefficient, by computation of another polynomial expression that indicates an amount of deformation of the EUV mask surface when flat correction is performed on the EUV mask by holding the EUV mask with the electrostatic pin chuck while the EUV mask is used in a scanning process; and
a third calculating unit that calculates a correction amount to correct the image displacement error of the EUV mask based on the calculated amount of image displacement error, by applying the coefficient.
2. The electron beam writing apparatus according to claim 1 , wherein a neutral plane of the EUV mask, which determines the amount of the image displacement error, is of a distorted surface represented in a symmetric function system, taking a position where the back surface of the EUV mask and the surface of the electrostatic pin chuck initially contact, as center coordinates.
3. The electron beam writing apparatus according to claim 1 , further comprising:
a reading unit that reads each of identification marks provided in EUV mask blanks,
wherein the first storing unit stores the identification marks and the back surface shape data therein in association with each other; and
a correction determination unit that performs determination as to whether writing is to be conducted, based on the correction amount of the amount of image displacement error when a corresponding identification mark is read by the reading unit.
4. The electron beam writing apparatus according to claim 3 , wherein a neutral plane of the EUV mask, which determines the amount of the image displacement error, is of a distorted surface represented in a symmetric function system, taking a position where the back surface of the EUV mask and the surface of the electrostatic pin chuck initially contact, as center coordinates.
5. The electron beam writing apparatus according to claim 3 , wherein the correction determination unit also uses data from a scanner using the EUV mask.
6. The electron beam writing apparatus according to claim 5 , wherein a neutral plane of an EUV mask, which determines the amount of the image displacement error, is of a distorted surface represented in a symmetric function system, taking a position where the back surface of the EUV mask and the surface of the electrostatic pin chuck initially contact, as center coordinates.
7. A method for correcting an image displacement error of an EUV mask based on a back surface shape of the EUV mask and a surface shape of an electrostatic pin chuck contacting the back surface of the EUV mask to hold the EUV mask on the electrostatic pin chuck, said method comprising:
storing surface shape data of the electrostatic pin chuck, comprising shape data of pins of the pin chuck, pitch data between the pins, and chucked region data, in a second storing unit;
storing back surface shape data obtained by measuring flatness of the back surface shape of the EUV mask, in a first storing unit;
reading the back surface shape data of the EUV mask from the first storing unit, and the surface shape data of the electrostatic pin chuck from the second storing unit;
extracting, via a data extraction unit, only a portion of the back surface shape data of the EUV mask using the surface shape data of the electrostatic pin chuck, the extracted portions of the back surface shape data of the EUV mask including only back surface shape data of the EUV mask at positions of the EUV mask that frictionally contact the pins of the electrostatic pin chuck;
performing, in a first calculating unit, an approximate computing process that approximates a shape of the EUV mask by a polynomial expression of only the extracted portion of the back surface shape data of the EUV mask extracted by the extracting;
determining a local tilt distribution at a back surface of the EUV mask, in a tilt calculating unit, from the polynomial expression that approximates the shape of the EUV mask using only the back surface shape data of the EUV mask at the positions of the EUV mask that frictionally contact the pins of the electrostatic chuck;
calculating an amount of image displacement error in a second calculating unit, based on the determined local tilt distribution and a predetermined amount of distortion where the back surface of the EUV mask is held by the electrostatic pin chuck when a pattern is written onto a front surface of the EUV mask;
obtaining a coefficient in a coefficient calculating unit, by computation of another polynomial expression that indicates an amount of deformation of the EUV mask surface when flat correction is performed on the EUV mask by holding the EUV mask with the electrostatic pin chuck while the EUV mask is used in a scanning process; and
calculating a correction amount to correct the image displacement error of the EUV mask based on the calculated amount of image displacement error, by applying the coefficient, in a third calculating unit.