Xuelian Zhu, Guanquan Liang, Yongan Xu, Shih-Chieh Cheng, and Shu Yang, "Fabrication of size scalable three-dimensional photonic structures via dual-beam multiple exposure and its robustness study," J. Opt. Soc. Am. B 27, 2534-2541 (2010)

We theoretically designed dual-beam triple exposure interference lithography to fabricate three-term diamond-like structures in SU-8 photoresist with scalable size and investigated the robustness of the optical setup against potential experimental errors. Minimal distortion could be achieved by careful selection of the angle between the bisector of the two beams and the normal of the sample surface to precompensate the anisotropic shrinkage. A small deviation of incident beam angles, however, would lead to a significant change in structural size when the angle between the two incident beams was small for a large sized structure, whereas the translational symmetry of the SU-8 structure remained reasonably close to face-centered cubic. We then experimentally demonstrate size scalable diamond-like photonic structures with the lattice symmetry and size close to the theoretical design.

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Pitch in (111) plane, ${a}_{xy}$$\left(\mu \text{m}\right)$

0.96

0.97

1.0

1.63

1.69

3.7

Periodicity in [111] direction ${a}_{z}$$\left(\mu \text{m}\right)$

2.35

2.19

6.9

3.98

4.08

2.4

Lattice constant d$\left(\mu \text{m}\right)$

1.36

1.34

1.6

2.30

2.38

3.4

Deviation of lattice symmetry $\left({a}_{z}/{a}_{z0}\right)$

1

0.92

1

0.99

For fcc lattice, the pitch in the (111) plane ${a}_{xy}=d/\sqrt{2}$, and the periodicity in the [111] direction ${a}_{z}=\sqrt{3}d$. For the rhombohedral lattice, the lattice constant $d={\left(4{a}_{xy}^{2}/3+{a}_{z}^{2}/9\right)}^{1/2}$. The relative deviation is defined as $\left|{c}_{\text{theo}}-{c}_{\text{exp}}\right|/{c}_{\text{theo}}$. To study the deviation of lattice symmetry from fcc, the experimental value of periodicity in the [111] direction ${a}_{z}$ is compared to the desirable one ${a}_{z0}=\sqrt{6}{a}_{xy}$.

Table 2

Wave Vectors and Polarization Vectors in Air and SU-8 Using Interference Lithography with Visible Light $\left(\lambda =532\text{\hspace{0.17em} nm}\right)$

Pitch in (111) plane, ${a}_{xy}$$\left(\mu \text{m}\right)$

0.96

0.97

1.0

1.63

1.69

3.7

Periodicity in [111] direction ${a}_{z}$$\left(\mu \text{m}\right)$

2.35

2.19

6.9

3.98

4.08

2.4

Lattice constant d$\left(\mu \text{m}\right)$

1.36

1.34

1.6

2.30

2.38

3.4

Deviation of lattice symmetry $\left({a}_{z}/{a}_{z0}\right)$

1

0.92

1

0.99

For fcc lattice, the pitch in the (111) plane ${a}_{xy}=d/\sqrt{2}$, and the periodicity in the [111] direction ${a}_{z}=\sqrt{3}d$. For the rhombohedral lattice, the lattice constant $d={\left(4{a}_{xy}^{2}/3+{a}_{z}^{2}/9\right)}^{1/2}$. The relative deviation is defined as $\left|{c}_{\text{theo}}-{c}_{\text{exp}}\right|/{c}_{\text{theo}}$. To study the deviation of lattice symmetry from fcc, the experimental value of periodicity in the [111] direction ${a}_{z}$ is compared to the desirable one ${a}_{z0}=\sqrt{6}{a}_{xy}$.

Table 2

Wave Vectors and Polarization Vectors in Air and SU-8 Using Interference Lithography with Visible Light $\left(\lambda =532\text{\hspace{0.17em} nm}\right)$