LITHOGRAPHY
53
drying steps. Proximity effects are caused by the Figure 2. Input and
combined chemical physical nature of dry etching output pattern
processes, including the shadowing effect for the features in a variable
ion flux, as well micro pattern density impacting etch bias model
the reaction kinetics. Interdependencies between
the proximity, mid range, and long range errors
are assumed to be negligible, so the error in the
mask critical dimension can be expressed in terms
of the proximity and long range components as:
Long range model
Long range mask CD uniformity errors include the
residual fogging effect in electron beam
lithography, resist develop, and pattern etch
loading [3, 6, and 7]. These errors are usually
described using a density loading model that
involves a convolution of the pattern density with a
Gaussian point spread function having a standard
deviation that is characteristic of the range of
influence. Long range mask CD errors are similarly
modelled using multiple Gaussian convolution capture long range process effects. Test patterns
terms. The systematic component of mask process used for proximity calibration are similar to
CD non uniformity is modelled by a polynomial patterns used building OPC models and are capable
term. The total long range mask CD errors can be of capturing both lithography and etch effects.
expressed as: Long range density loading test patterns
composed of lines and spaces are arranged
horizontally across the mask and embedded in
regions having varying pattern area density.
Process uniformity test structures are distributed
in a regular array over the entire pattern, and are
surrounded by regions with constant area density
to minimise the effects of pattern density on the
Short range model uniformity measurements.
The short range mask process model describes the The proximity calibration pattern includes Figure 3. Example
short range effects in electron beam lithography various combinations of lines and spaces, end to test mask design for
and pattern etching and leverage the experience in end line and space structures, posts, and contacts. proximity and long
optical proximity correction (OPC). Assuming that Several arrays of these patterns are placed on the range MPC
the residual effects are mainly driven by etch mask when modeling. calibration [9]
processes, the method is based on an etch model
proven in wafer process correction applications,
specifically a variable etch bias (VEB) model [5,
8]. VEB models can contain additional Gaussian
terms convolved with the mask pattern to capture
the patterning errors due to electron beam
lithography. The position dependent bias ‘b’
resulting from applying the VEB model to an input
mask pattern shape is shown in Figure 2.
Model calibrated test patterns
Test patterns designed specifically for measuring
the different sources of error are needed to ensure
an accurate description of the mask process. A
typical MPC test pattern is shown in Figure 3. The
overall pattern spans the whole area of interest to
the mask process, and process uniformity and
pattern density loading patterns are employed to
November 2008
www.euroasiasemiconductor.com
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