Generation of arbitrary lithographic patterns using Bose-Einstein-condensate interferometry

We propose an arbitrary pattern lithography process using interference of Bose-Einstein condensates (BECs). A symmetric three-pulse Raman atom interferometer (AI) is used to implement the system. The pattern information, in the form of a phase-only mask, is optically encoded into the BEC order parameter in one of the AI arms. The lithographic pattern is represented by a two-dimensional intensity variation, and is transformed into a two-dimensional phase variation in the BEC order parameter via the use of ac-Stark shift induced by a pulsed laser field. The BEC probability distribution of the interference result at the end of the AI is proportional to the required pattern. In order to produce features smaller than the diffraction limit for the used optical elements, we employ a three-dimensional atomic lens system to scale down the resulting pattern. The operating conditions for this lens structure are investigated in order to identify practical constraints. Simulations of the overall system using the parameters of ${}^{87}\mathrm{Rb}$ BEC were performed to illustrate its functionality. The proposed process, while perhaps not suitable for general purpose usage, may enable the creation of special purpose patterns on a very small scale, with features as small as a few nanometers.

Figure 1

Architecture of two-dimensional (2D) lithography system using BEC. See text for details.

Figure 2

Three-level system used by the atom interferometer. See text for details.

Figure 3

The proposed technique to imprint spatially varying phase pattern to a BEC. See text for details.

Figure 4

(a) Fourier transform atomic lens scheme. (b) Proposed implementation to create three-dimensional phase shift. See text for details.

Figure 5

Atom lithography system with the implementation of the lenses shown explicitly. ${\mathrm{\Phi }}_{\mathrm{p}}$ is the pattern phase shift. See text for details.

Figure 6

Proposed simplification of the lens system. See text for details.

Figure 7

Simplified atom lithography system. See text for details.

Figure 8

Laser interactions required for the proposed atom lithography system. (a) Laser interactions required for the Raman AI (solid lines). (b) Ac-Stark interactions required to implement the lens system for both AI arms (dashed lines). See text for details.

Figure 9

(a) The required lithographic pattern. (b) The resulting distribution of the order parameter after the atomic interferometer.

Figure 10

Comparison between the $x$ cross section of the single-atom wave function and the BEC order parameter after a free space propagation of 1 s.

Figure 11

Cross section of the BEC order parameter after different configurations of the lens system.

Figure 12

Result of the lithography system using the simplified lens configuration. (a) Required lithographic pattern. (b) Normalized effective 2D probability distribution for unity scaling (c) for a scaling ratio of 0.8 and (d) for a scaling ratio of 2/3.

Figure 13

Normalized effective 2D probability distribution for a plus sign pattern using the original lens system (a) with unity scaling and (b) with a scaling ratio of 0.8.

Figure 14

Results of the lithography system for a circular pattern using the simplified lens system; (a) the desired circular pattern. (b) Normalized effective 2D probability distribution for the unity scaling case. (c) Result for a scaling ratio of 0.8. (d) Result for a scaling ratio of 2/3.

Figure 15

Results of the lithography system for a circular pattern using the original lens arrangement. (a) Normalized effective 2D probability distribution for unity scaling and (b) for a scaling ratio of 0.8.

Figure 16

Results of the lithography system for a letter $\mathsf{n}$ pattern using the modified lens arrangement. (a) The desired letter $\mathsf{n}$ pattern. (b) Normalized effective 2D probability distribution for the unity scaling case. (c) Result with a scaling ratio of 0.8. (d) Result with a scaling ratio of 2/3.

Figure 17

Results of the lithography system for a circular pattern for two different numerical simulation resolutions: (a) the spatial step $\mathrm{size}=0.05\sigma$ and (b) the spatial step $\mathrm{size}=0.0625\sigma$, where σ is the standard deviation of the initial order parameter Gaussian distribution.