Source: https://patents.google.com/patent/US7649615B2/en
Timestamp: 2019-08-22 01:45:41
Document Index: 25589815

Matched Legal Cases: ['application No. 60', 'application No. 60', 'application No. 60', 'application No. 60', 'application No. 60', 'application No. 60']

US7649615B2 - Advanced exposure techniques for programmable lithography - Google Patents
US7649615B2
US7649615B2 US11/797,351 US79735107A US7649615B2 US 7649615 B2 US7649615 B2 US 7649615B2 US 79735107 A US79735107 A US 79735107A US 7649615 B2 US7649615 B2 US 7649615B2
US11/797,351
US20070258071A1 (en
2005-12-23 Priority to US11/315,136 priority patent/US20060098181A1/en
2007-05-02 Priority to US11/797,351 priority patent/US7649615B2/en
2007-05-02 Application filed by Pixelligent Technologies LLC filed Critical Pixelligent Technologies LLC
2007-11-08 Publication of US20070258071A1 publication Critical patent/US20070258071A1/en
2010-01-19 Publication of US7649615B2 publication Critical patent/US7649615B2/en
application No. 60/330,765 filed Oct. 30, 2001 entitled “Pattern Decomposition”;
application No. 60/330,745 filed Oct. 30, 2001 entitled “Programmable Phase-Shifting”;
application No. 60/331,038 filed Nov. 7, 2001 entitled “Pattern Decomposition”;
application No. 60/331,039 filed Nov. 7, 2001 entitled “Programmable Phase-Shifting”; and
application No. 60/331,515 filed Nov. 19, 2001 entitled “Method and Apparatus For Exposing Photoresists Using Programmable Masks”.
This application is also related to commonly-assigned application Ser. No. 09/871,971, now U.S. Pat. No. 6,480,261 B2, to Cooper et al. entitled “Photolithographic System For Exposing A Wafer Using A Programmable Mask” and filed Jun. 4, 2001 incorporated by reference herein.
These various techniques can be used independently, together in any combination, and/or in combination with other techniques (e.g., photoresist exposure techniques such as disclosed in our commonly-assigned application Ser. No. 10/298,224 filed Nov. 18, 2002, now U.S. Pat. No. 6,879,376, based on provisional application No. 60/331,515 filed Nov. 19, 2001), to improve performance such as resolution of programmable photolithography.
X ~ = ( 9 16 - 3 8 3 16 - 3 8 1 4 - 1 8 3 16 - 1 8 1 16 3 16 3 8 - 3 16 - 1 8 - 1 4 1 8 1 16 1 8 - 1 16 - 3 16 3 8 3 16 1 8 - 1 4 - 1 8 - 1 16 1 8 1 16 3 16 - 3 8 9 16 - 1 8 1 4 - 3 8 1 16 - 1 8 3 16 3 16 - 1 8 1 16 3 8 - 1 4 1 8 - 3 16 1 8 - 1 16 1 16 1 8 - 1 16 1 8 1 4 - 1 8 - 1 16 - 1 8 1 16 - 1 16 1 8 1 16 - 1 8 1 4 1 8 1 16 - 1 8 - 1 16 1 16 - 1 8 3 16 1 8 - 1 4 3 8 - 1 16 1 8 - 3 16 - 3 16 1 8 - 1 16 3 8 - 1 4 1 8 3 16 - 1 8 1 16 - 1 16 - 1 8 1 16 1 8 1 4 - 1 8 1 16 1 8 - 1 16 1 16 - 1 8 - 1 16 - 1 8 1 4 1 8 - 1 16 1 8 1 16 - 1 16 1 8 - 3 16 1 8 - 1 4 3 8 1 16 - 1 8 3 16 3 16 - 1 8 1 16 - 3 8 1 4 - 1 8 9 16 - 3 8 3 16 1 16 1 8 - 1 16 - 1 8 - 1 4 1 8 3 16 3 8 - 3 16 - 1 16 1 8 1 16 1 8 - 1 4 - 1 8 - 3 16 3 8 3 16 1 16 - 1 8 3 16 - 1 8 1 4 - 3 8 3 16 - 3 8 9 16 ) so ⁢ ⁢ that A ~ · X ~ = ( 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 ) = I ~ 9 × 9
The matrix {tilde over (X)} may be found using well known techniques (for example, the Mathematica function Pseudolnverse
calculates {tilde over (X)} given Ã). This leaves the condition that
Finally, some comments on the nature of {tilde over (T)}—this is the vector that permits tweaking of the solution: In practice, the thing we add to the solution in our exemplary illustrative non-limiting implementation is not {tilde over (T)}, but (Ĩ−Ã·{tilde over (X)})·{tilde over (T)}. This vector has no effect on the derived values for {right arrow over (E)} because it lies in the null space of the operator Ã. The operator (Ĩ−Ã·{tilde over (X)}) projects any vector into the null space of Ã. With this observation, we can simplify the equation for a solution to {right arrow over (E)}={tilde over (X)}·{right arrow over (G)}+{right arrow over (T)}N(A), where {tilde over (T)}N(A) is any vector lying in the null space of Ã. Using standard techniques we can calculate a set of vectors spanning the null space of Ã, and therefore construct a basis for {tilde over (T)}N(A). It is entirely possible that our pseudo inverse is such that there is no null space (i.e. Ã·{tilde over (X)}=Ĩ), in which case we have to turn to other methods of tweaking the exposure values, such as adjusting the grid pattern vector {right arrow over (G)} for example.
where d is the feature size (d can also be the feature separation), λ is the wavelength, NA is the numerical aperture, and k1 is a process constant. Values of k1 as low as 0.1 have been reported when treated as a process constant. In conventional lithography the pitch (feature size+feature separation) may be greater than 0.5λ/NA.
n(E)=n 0 +·E
a ⁡ ( x ) = ∫ - β 0 β 0 ⁢ ⁢ ⅆ β ⁢ ⁢ U ⁡ ( β ) ⁢ exp ⁡ ( jβ ⁢ ⁢ x )
N n = ∫ - 1 1 ⁢ ⁢ ⅆ t ⁡ [ S 0 ⁢ n ⁡ ( c , t ) ] 2
a ⁡ ( x ) = ∑ n = 0 ∞ ⁢ λ n - 1 ⁢ ψ n ⁡ ( 0 ) ⁢ ψ n ⁡ ( x )
U ⁡ ( β ) = ( x 0 / 2 ⁢ πβ 0 ) 1 / 2 ⁢ ∑ n = 0 ∞ ⁢ j n ⁢ λ n - 1 ⁢ ψ n ⁡ ( 0 ) ⁢ ψ n ⁡ ( β ⁢ ⁢ x / β 0 )
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