Modeling of EUV photoresists with a resist point spreadfunction Page: 2 of 9
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2. RESIST POINT SPREAD FUNCTION MODEL
An accurate model of the photoresist response is extremely useful for process development, control, and other
applications. These models are often complex systems of differential equations, making them fairly computationally
intensive. A much simpler resist modeling technique using a resist point spread function4 has been shown to have good
agreement with experiments for certain EUV resists such as Shipley EUV-2D.5 The resist point spread function is a
two-dimensional function that, when convolved with the simulated aerial image for a given mask pattern and applied to a
threshold function, gives a representation of the photoresist pattern remaining after development. This is summarized
for positive resists in Equation 1:
1, Iaeria(x, y) O PSFess,(x,y)<T
rresst.YJ L0, otherwise ' 1
where Iesst(x,y) is the (binary) resist image intensity, Iaenai(x,y) is the aerial image intensity, PSFres1st(x,y) is the resist
point spread function (PSF), and T is the resist threshold. The same relationship holds for negative resists if the "less
than" symbol is changed to a "greater than" symbol. Note that because a simple threshold approach is used to determine
the resist image, only first-order effects such as feature size can be predicted using this model. Therefore, second-order
effects such as sidewall angle or feature height cannot be predicted.
3. EXTRACTION OF RESIST POINT SPREAD FUNCTION
The resist point spread function may be extracted from measurements of the contrast transfer function (CTF) for the
optical system used for resist exposures. The first step in the procedure is to select the form for the point spread
function. In this work a Gaussian function is used. Because the PSF is being fit to one-dimensional features (the equal-
width lines and spaces used to measure CTF), it is only necessary to use a one-dimensional Gaussian of the form
PSFess,(x) = Ie (2F
where aPSF is the standard deviation of the Gaussian function used for the resist PSF. Note that the full width at half
maximum (FWHM) of the resist PSF is related to aPSF by
FWHM =2 21n 2JPSF. (3)
This is equivalent to measuring a cross-section of the PSF in the direction perpendicular to the lines and spaces. In
this case, the PSF is assumed to be rotationally symmetric. However, the two-dimensional PSF may be reconstructed by
measuring the CTF for lines of different orientations and fitting the data individually. Under the assumption that
anisotropy is not present in the resist, this additional measurement is not required.
In order to extract the resist PSF for a given resist, the measured CTF and the simulated CTF (including effects of
optical aberrations and illumination conditions) are required. In order to account for any constant "DC offset"' between
the measured and simulated CTF, a variable parameter, FDC, is subtracted from each point in the simulated CTF curve
before the convolution step. The FDC term may be considered another model parameter that may be varied to obtain the
best fit. For each feature size (or spatial frequency) in the measured data, a sinusoid of appropriate pitch is generated
with a contrast matching the corresponding simulated value. The sinusoid is then convolved with the chosen resist PSF
function, and the contrast of the result is compared with the measured value. The parameters of the resist PSF may be
varied in order to find the values that best fit the measured data. In the case of a one-dimensional Gaussian resist PSF,
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Cain, Jason P.; Naulleau, Patrick & Spanos, Costas J. Modeling of EUV photoresists with a resist point spreadfunction, article, January 1, 2005; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc884329/m1/2/: accessed February 15, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.