Resonant Interferometric Lithography beyond the Diffraction Limit

A novel approach for the generation of subwavelength structures in interferometric optical lithography is described. Our scheme relies on the preparation of the system in a position dependent trapping state via phase shifted standing wave patterns. Since this process only comprises resonant atom-field interactions, a multiphoton absorption medium is not required. The contrast of the induced pattern does only depend on the ratios of the applied field strengths such that our method in principle works at very low laser intensities.

Figure 1

Considered level schemes of the photoresist. The ground states $|g_n⟩$ and $|g_{n+1}⟩$ are resonantly coupled to the excited state $|e_n⟩$ via Rabi frequencies ${\mathcal{R}}_n$ and ${\mathcal{S}}_n$, respectively. Each excited state $|e_n⟩$ decays to the ground states $|g_n⟩$ and $|g_{n+1}⟩$ by spontaneous emission. (a) Single $\Lambda$ system. In (b), a sequence of two $\Lambda$ systems is displayed. (c) General level scheme with $N$ excited and $N+1$ ground states as a sequence of $N$ $\Lambda$-type systems.

Figure 2

(a) Each standing wave pattern ${\mathcal{R}}_n$, ${\mathcal{S}}_n$ is formed by two plane waves ${\mathcal{X}}_i$, ${\mathcal{Y}}_i$ with wavelength ${\lambda }_i$. The period of each intensity pattern is given by ${\lambda }_0/2$, where ${\lambda }_0={\lambda }_i/\cos {\theta }_i$, and ${\theta }_i$ is chosen such that the effective wavelength in the substrate plane is equal to ${\lambda }_0$ for all ${\mathcal{R}}_n$ and ${\mathcal{S}}_n$. Subfigures (b) and (c) correspond to the $M$ system shown in Fig. 1b. Part (b) illustrates the intensity profiles of the standing waves ${\mathcal{R}}_n$ and ${\mathcal{S}}_n$ ($n=1$, 2) according to Eq. (9). Note that $|{\mathcal{R}}_n{|}^2$ and $|{\mathcal{S}}_n{|}^2$ are not drawn to scale. The solid line in (c) shows the population of state $|g_1⟩$ corresponding to Eqs. (10, 12) with $\eta =1/20$. It varies with wave number $4k_0$. The dotted line is the corresponding result with nonzero ground state decoherence rates ${\gamma }_{\mathrm{coh}}$. We set ${\gamma }_{\mathrm{coh}}=\gamma$, where $\gamma$ is the full decay rate on the $|e_n⟩\leftrightarrow |g_{n\pm 1}⟩$ transition.