Image analysis – Applications – Manufacturing or product inspection
Reexamination Certificate
1999-06-14
2002-09-10
Mancuso, Joseph (Department: 2623)
Image analysis
Applications
Manufacturing or product inspection
C382S145000, C430S005000
Reexamination Certificate
active
06449387
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a technique for analyzing light intensity distribution on an light exposure area where a mask pattern will be projected.
2. Description of the Related Art
A semiconductor device manufacturing process includes the photolithography step of shaping a photoresist film formed on a wafer into the desired form by a patterning technique. In this photolithography step, as illustrated in
FIG. 4
, light coming from a light source
11
passes through a mask
12
and is thereafter condensed by a lens
13
so as to be projected onto the photoresist film
14
formed on the wafer
15
. However, the resultant resist pattern on the wafer
15
does not always have the same shape as a pattern printed on the mask
12
. In consideration of this, the pattern needs to be printed on the mask
12
so that the resist pattern projected on the wafer
15
will be within an allowable design range.
To this end, the correspondence between the pattern printed on the mask and the resist pattern needs to be grasped. According to a conventionally known method, the intensity of light which will be projected on a light exposure area of a wafer to be exposed to light is analyzed through simulation, without the photoresist film being actually subjected to light.
The document “Y. C. Pati. et al. J. Opt. Soc. Am. A/Vol. 11, No. 9, 1994 ” discloses a light intensity calculating method for use in the case where the optical simulation of a stepper optical system, which is a kind of light exposure apparatus, is executed as such photolithographic simulation. According to the OCA (Optimal Coherent Approximation) method disclosed thereby, the light intensity (x, y) at the position specified by coordinates (x, y) on the light exposure area of the wafer is expressed by Equation (1) shown below:
I
(
x, y
)=&Sgr;&agr;|(
F
×&phgr;)(
x, y
)|
2
(1)
where &agr; and &phgr; represent optical kernels determined by the stepper optical system (light exposure apparatus), F represents the transmission factor of the mask, and (F×&phgr;(x, y) is the convolution integral of F and &phgr;.
A conventional light intensity analyzing method which adopts Equation (1) shown above will now be described with reference to the flowchart of FIG.
5
. The process shown in this flowchart is executed by an information processing apparatus such as an engineering workstation.
Firstly, the kernel &phgr; corresponding to each set of coordinates (x, y) on a wafer surface area when divided into a grid of areas at predetermined grid intervals dx
f
, are calculated and stored in a table (a step S
201
). The kernel &phgr; is a value representing the extent of the mask which optically influences the coordinates (x, y) on the wafer. A rectangular area (S
k
×S
k
), which has the size (S
k
) equal to the kernel &phgr; associated with a given set of coordinates (x, y), and which is located at a position corresponding to that specified by the given set of coordinates (x, y), is cut out from the mask pattern (a step S
202
).
Next, data representing the shape of the mask is developed into a bit map at grid intervals dx
f
, and the transmission factor F of the mask at the rectangular area is obtained (a step S
203
). The convolution integral (F×&phgr;) (x, y) of the transmission factor F and the kernel &phgr; is calculated and the calculated integral is adopted in Equation (1), thus obtaining the light intensity I (x, y) at the position specified by the given set of coordinates (x, y) on the wafer (a step S
204
).
Thereafter, it is determined whether the light intensities I (x, y) at the positions on the wafer, which positions are specified by all sets of target coordinates (x, y), have been calculated or not (a step S
205
). If it is determined that the light intensities I (x, y) at the positions specified by all sets of target coordinates (x, y) have not yet been calculated, then the same calculation as that described above is performed in connection with the position specified by the next set of coordinates. On the other hand, if it is determined that the light intensities I (x, y) at the positions specified by all sets of target coordinates (x, y) have been calculated, the entire light intensity distribution is output as the result of the analysis (a step S
206
). Then, the process shown in the flowchart is terminated.
However, in the case of analyzing the light intensity distribution with the conventional method described above, the grid intervals dx
f
at which the shape of the mask is developed into the bit map needs to be set at a satisfactorily small value in order to correctly evaluate the shape of the resist pattern which will be formed on the wafer. When calculating the convolution integral of the transmission factor F in connection with each of the rectangular areas divided at fine grid intervals set at such a small value, the calculation time is considerably long and the time required for the analysis is accordingly long.
Japanese Patent No. 2531114 and Unexamined Japanese Patent Application KOKAI Publication No. H9-237750 disclose light intensity distribution analyzing methods intended to reduce the time required for the analysis of the light intensity distribution. However, according to the methods disclosed thereby, the light intensity distribution is analyzed using Fourier transform. The techniques disclosed by the above patent and publication cannot be adopted as they are in a method for calculating the light intensity through utilization of the convolution integral.
SUMMARY OF THE INVENTION
It is accordingly an object of the present invention to provide a method and an apparatus which are capable of analyzing the light intensity distribution on a light exposure area within a short period of time, and a computer program product including a computer usable medium which contains a computer readable program embodied therein for the analysis of the light intensity distribution.
According to the first aspect of the present invention which aims to achieve the above object, there is provided a method for analyzing light intensity distribution on a light exposure area where a shape of a mask pattern will be projected through an optical system by exposure light coming from a light source, the analyzing method comprising:
dividing the light exposure area into first areas at predetermined first intervals;
cutting out first portions of the mask pattern which correspond to the first areas;
sequentially determining whether transmission areas which transmit the exposure light and non-transmission areas which do not transmit the exposure light are mingled at the cut-out first portions of the mask pattern;
calculating intensities of light which will be projected on the light exposure area, through use of the first portion of the mask pattern, when it is determined that the transmission areas and the non-transmission areas are not mingled; and
dividing each of the first areas into second areas at second intervals smaller than the first intervals and calculating intensities of light which will be projected on the light exposure area, through use of second portions of the mask pattern which correspond to the second areas, when it is determined that the transmission areas and the non-transmission areas are mingled.
According to the above method, only in the case where the transmission areas and the non transmission areas are mingled at the first portions of the mask pattern, the light intensity is calculated through use of the second portions of the mask pattern which correspond to the second areas into which each of the first areas have been divided. In the case where the transmission areas and the non transmission areas are not mingled, the light intensity is calculated through use of the first portions of the mask pattern which correspond to the first areas. Because of this, the number of times the light intensity calculation is performed to analyze the light intensity distribution over the entirety of the light exposure area is red
Bali Vikkram
Mancuso Joseph
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