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J. Eur. Opt. Society-Rapid Publ. 22, 9( 2026)
Figure 2. Left: Principle sketch of SBIL setup with two mirrors. Right: Simulation of SBIL in x-direction with different disturbances. The first scenario shows a perfect scan without disturbances. The second scenario shows the case in which the fringes in the exposure pattern move up and down alternately due to phase fluctuations and generate curved paths. In the next scenario, the angle of incidence drifts during scanning. This changes the period of the fringe during the exposure. In the last scenario, the fringe pattern is rotated to the scan direction, thus leads to poor dose contrast during exposure.
or pattern rotations occur, the resulting blurring or misalignment of the interference fringes leads to a reduced local intensity gradient. This causes a loss of dose contrast in the photo resist, making it more difficult to achieve sharp and uniform feature development.
The fringe period p is defined by the incident angles h 1, h 2 and the wavelength k of the two exposure beams:
p ¼ k sinðh 1 Þ�sinðh 2 Þ; h 1 > 0; h 2 < 0: ð1Þ
The intensity distribution of the two interfering exposure beams in one dimension with equal polarization state is given as
I ðx; tÞ ¼ðE 1 þ E 2 ÞðE 1 þ E 2 Þ pffiffiffiffiffiffiffiffiffiffiffiffi
¼ I 1 þ I 2 þ 2 I 1 I 2 cos½uðxÞþu th ðtÞŠ; ð2Þ
where Du( x) is the initial phase difference between the two exposure beams and u th( t) the time-dependent thermal phase fluctuation that causes the fringe shift. The Michelson contrast of the interference pattern is defined as
C I ¼ I max � I min: ð3Þ
I max þ I min
While the position x of the fringes changes over the exposure time t exp, the intensity in the photoresist is integrated, with the dose being defined by
DðxÞ ¼
Z texp
0
I ðx; tÞ dt: ð4Þ
The fringe shift by time results in a loss of dose contrast. The dose contrast is expressed as
C D ¼ D max � D min D max þ D min
: ð5Þ
Figure
3. Dose contrast loss for a dislocation function u th = A sin( x t). The maximum dislocation increases from zero to a quarter period of the intensity distribution.
This value quantifies the exposure process in the photoresist. A dose contrast loss simulation is shown in Figure 3. For illustration we define a sinusoidal function. Therefore the function is defined as follows:
u th ¼ A sinðx tÞ: ð6Þ
x is the shift frequency and t the exposure time. The amplitude A defines the maximum fringe shift and for the dose contrast simulation in Figure 3, A increases from zero to a quarter period of the intensity distribution, so that the dose contrast is halved. With equations( 6),( 2),( 4) and( 5) the loss can be calculated for different dislocation amplitudes. The integration of x t for the dose simulation is over one period.
3 Experimental setup
The writing head is designed to be installed in the nanopositioning and measuring machine NPMM-200, which is installed at the Institute of Applied Optics [ 21 ]. The stage in which the substrate can be placed is controlled by six interferometers. This provides high-precision distance and rotation measurement for six degrees of freedom and control for five degrees of freedom. The nano-scale positioning