No abstract

The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.

Articles you may be interested inExploring the ultimate resolution of positive-tone chemically amplified resists: 26 nm dense lines using extreme ultraviolet interference lithography J. Vac. Sci. Technol. B 22, 99 (2004); 10.1116/1.1640402 Fabrication of sub-50 nm critical feature for magnetic recording device using electron-beam lithography Magnetic information storage density has increased at the rate of 60% per year for the past seven years. There is wide agreement that continuation of this trend beyond the physical limits of the continuous thin-film media currently used will likely require a transition to discrete, lithographically defined magnetic pillars. Interference lithography ͑IL͒ appears to be the most cost-effective means of producing two-dimensional arrays of such pillars. IL can rapidly expose large areas with relatively simple equipment, without the need for a mask, and with fine control of the ratio of pillar diameter to period. We show that negative-tone imaging yields three times the contrast of positive-tone imaging for the generation of holes in photoresist, suitable for subsequent deposition or electroplating of magnetic material. We use a negative i-line, chemically-amplified resist ͑OHKA THMR-iN PS1͒ to form 200 nm period arrays of magnetic dots in Co and Ni. Such arrays, with a variety of well controlled diameters, are used to study the effect of particle size on magnetic behavior.

Pattern-placement metrology plays a critical role in nanofabrication. Not far in the future, metrology standards approaching 0.2 nm in accuracy will be required to facilitate the production of 25 nm semiconductor devices. They will also be needed to support the manufacturing of high-density wavelength-division-multiplexed integrated optoelectronic devices. We are developing a new approach to metrology in the sub-100 nm domain that is based on using phase-coherent fiducial gratings and grids patterned by interference lithography. This approach is complementary to the traditional mark-detection, or ''market plot'' pattern-placement metrology. In this article we explore the limitations of laser-interferometer-based mark-detection metrology, and contrast this with ways that fiducial grids could be used to solve a variety of metrology problems. These include measuring process-induced distortions in substrates; measuring patterning distortions in pattern-mastering systems, such as laser and e-beam writers; and measuring field distortions and alignment errors in steppers and scanners. We describe a proposed standard for pattern-placement metrology, which includes both a fiducial grid and market-type marks. Finally, a number of methods through which phase-coherent periodic structures can be patterned are shown, including ''traditional'' interference lithography, achromatic interference lithography, near-field interference lithography, and scanning-beam interference lithography.

We present here a hybrid approach to modeling helium-ion lithography that combines the power and ease-of-use of the Stopping and Range of Ions in Matter (SRIM) software with the results of recent work simulating secondary electron (SE) yield in helium-ion microscopy. This approach traces along SRIM-produced helium-ion trajectories, generating and simulating trajectories for SEs using a Monte Carlo method. We found, both through simulation and experiment, that the spatial distribution of energy deposition in a resist as a function of radial distance from beam incidence, i.e. the point spread function, is not simply a sum of Gauss functions.Preprint in press, Scanning (journal website: http://dx