Proximity Effect In Electron Beam Lithography Research Articles

Proximity effect correction in electron-beam lithography based on computation of critical-development time with swarm intelligence

Electron-beam lithography (EBL) is an important technique in manufacturing high-resolution nanopatterns for broad applications. However, the proximity effect in EBL can degrade the pattern quality and, thus, impact the performance of the applications greatly. The conventional proximity effect correction (PEC) methods, which employ computationally intensive cell or path removal method for development simulation, are very computational lengthy, especially for complex and large-area patterns. Here, the authors propose a novel short-range PEC method by transforming the evaluation of pattern feasibility into the shortest path problem based on the concept of critical-development time. The authors combine this evaluation algorithm with the swarm intelligence which mimics the natural collective behavior of animals to optimize the design of electron dose distribution in EBL. The PEC algorithm is applied for pattern fabrication for U-shaped split-ring resonator and produces optimized exposure pattern that shows excellent agreement with the targeted objectives. Our work on the PEC strategy reduces the computational cost significantly and is particularly suitable for the design of complex pattern with various constraints.

Fabricating a silicon nanowire by using the proximity effect in electron beam lithographyfor investigation of the Coulomb blockade effect

We present an approach to fabricate a silicon nanowire relying on the proximity effect inelectron beam lithography with a low acceleration voltage system by designing theexposure patterns with a rhombus sandwiched between two symmetric wedges. Thereproducibility is investigated by changing the number of rhombuses. A device with asilicon nanowire is constructed on a highly doped silicon-on-insulator wafer to measure theelectronic transport characteristics. Significant nonlinear behavior of current–voltage curvesis observed at up to 150 K. The dependence of current on the drain voltage and back-gatevoltage shows Coulomb blockade oscillations at 5.4 K, revealing a Coulomb island naturallyformed in the nanowire. The mechanism of formation of the Coulomb island isdiscussed.

Small angle X-ray scattering measurements of spatial dependent linewidth in dense nanoline gratings

Small angle X-ray scattering (SAXS) was used to characterize the cross section of nanoline gratings fabricated with electron beam lithography (EBL) patterning followed by anisotropic wet etching into a single crystal silicon substrate. SAXS results at normal incidence clearly bear the signature of positional dependent linewidth within the gratings; such non-uniformity is subsequently confirmed with scanning electron microscopy. The proximity effect of EBL is believed to be the cause of the spatial variations of linewidth. To quantitatively fit the SAXS results the linewidth near the periphery of the patterned field needs to be 80% greater than that in the central region, whereas the cross section of nanolines can be modeled as a simple rectangular shape, as expected from the anisotropic wet etching process.

Influence of proximity effects in electron-beam lithography on the optical properties of planar photonic-crystal waveguides

To measure the influence of proximity effects in electron-beam lithography on the optical properties of planar photonic crystal (PPC) waveguides we propose a PPC structure called the “PECmeter.” The PECmeter consists of nearly identical PPC waveguides which only differ in the number of rows of holes along the waveguide. The difference in the number of rows does not influence the modal properties directly but changes the diameter of the holes neighboring the waveguide through the proximity effect. The operation principle of the PECmeter is demonstrated using energy-intensity simulations of a W3 waveguide (three missing rows of holes) mini stop band. The principle is confirmed experimentally with structures fabricated in the InP-based material system and measured by the end-fire transmission technique. The results clearly show that the application of proximity-effect correction (PEC) is crucial for the fabrication of PPC waveguides. We demonstrate that when using the midpoint-equalization PEC method a near-to-perfect correction with sub-nm hole-radius uniformity can be achieved. We show the PECmeter to be sensitive enough to detect hole-radius changes as small as ΔR=0.4 nm.

Monte Carlo simulation of process parameters in electron beam lithography for thick resist patterning

To better understand the proximity effect of electron-beam lithography and its limitation on aspect ratios in a thick resist film (>1.0μm), the simulation of isolated trench patterning has been performed using the Monte Carlo simulation software SELID™. Various key process parameters, including beam energy, exposure dose, substrate, acid diffusion length, and development time have been analyzed by means of the point-spread function, secondary electron distribution, energy distributions, and developed resist profiles. Exposure dose and development time are optimized to achieve vertical sidewalls, and the acid diffusion length has been adjusted to slightly change the top and bottom dimensions of the patterned trench. The simulation results show that increasing the beam energy significantly reduces the forward proximity effect and thereby increases the trench aspect ratio. In contrast, the substrate generally has only a minor effect in terms of the resist profile because its backscattering effect covers a long range up to 10.0μm from incident point (50keV). The achievable maximum aspect ratio for a given resist thickness was found to scale approximately linearly with beam energy. The aspect ratio in a 1.0μm thick resist film increased from 3:1 to 20:1 as the beam energy was increased from 10to100keV, and from 5:1 to 10:1 for a 4.0μm resist film as the beam energy was increased from 50to100keV. Finally, experimental data using a 50keV Leica e-beam writing tool is presented, and they agree with the results from our simulations.

Analysis of three-dimensional proximity effect in electron-beam lithography

In most of the proximity effect correction schemes, a two-dimensional model of proximity effect is employed by ignoring or averaging the variation of exposure along the depth dimension in the resist. However, as the feature size continues to decrease, the relative variation becomes significant so that it may need to be taken into account in proximity effect correction. In this study, the three-dimensional (3-D) proximity effect is analyzed in detail through computer simulation as a first step toward developing a 3-D proximity effect correction scheme. Effects of the parameters such as beam energy, resist thickness, feature size, developing threshold, etc., on the 3-D spatial distribution of exposure in the resist, in particular, depth-dependent proximity effect, are considered in the analysis. Results from the extensive simulation are presented in this paper.

Lateral spreads of energy dissipation profiles of 20-kV electrons in polymethylmethacrylate: Functional representation and its application to proximity effect

Monte Carlo calculations have been used extensively to study the energy dissipation of electrons penetrating into solid materials both in the direction of the initial electron trajectory and lateral to it. Knowing the lateral energy dissipation is important for the prediction of proximity effects in electron-beam lithography and limiting resolution in scanning electron microscopy. The Weibull probability density functions are shown to approximate the lateral energy dissipation profiles determined by Monte Carlo calculations of 20-keV electrons in polymethylmethacrylate (PMMA), and their application to simple line and square patterns of electron-beam exposure are also discussed.

Proximity Correction Enhancements for 1-µm Dense Circuits

The proximity effect in electron-beam lithography, which is due to electron scattering in the resist and wafer, results in nonuniform exposure and development for patterns in which the incident doses of all the shapes are the same. Correction for this effect has been accomplished in the past primarily by varying the incident doses of all the shapes in order to achieve an equal average resultant dose per unit area for all shapes. We show that in the case of dense circuits with linewidths of about 1 µm or smaller, two enhancements to the proximity correction technique can be easily implemented. One of these is a simple approach to shape breakup (partitioning) to enable dose correction to be applied nonuniformly within the original design shapes. The other technique is a new type of algorithm for forming subsets of the design to perform self-consistent dose correction. These two enhancements are applied to LSI chip data for dense circuits and are shown to permit fabrication of circuits which would be more difficult to process using the proximity correction techniques described previously, due to the particular geometries present in these circuit designs. We also show the application of step and repeat pattern recognition algorithms to compact the resulting data, and consequently to reduce the amount of data by an amount which is greater than the increase in the number of shapes caused by partitioning.

Fast computation method for exposure intensity and pattern correction in electron-beam lithography

A fast computation method to correct for the proximity effect in electron-beam lithography is studied for practical uses. Formerly, to compute the proximity effect a double integral of two Gaussian distribution functions was applied. To save computation time and memory size, a simplified computation using the error function is discussed. In this solution the proximity effect correction is determined by two real multiplications, four subtractions and one addition. Not only beam intensity but also a pattern element size is considered in every pattern. A large pattern is divided into small sections. In this method, the computation time is proportional to the number of elements. It takes 105 minutes to compute 10 000 test pattern elements with a minicomputer. The experiment proves that the corrected pattern can be exposed as designed. This procedure has proven effective to design VLSI by using a minicomputer.

Energy deposition functions in electron resist films on substrates

A Monte Carlo simulation of electron scattering in the resist and substrate of a target in electron lithography was used to obtain the spatial distribution of energy deposition in the resist. Analytical approximations were subsequently obtained by a least-squares fit of Gaussian functions to the forward- and backward-scattered components of these distributions. The parameters in the analytical functions were deduced and a compendium of values are tabulated for a variety of resist thicknesses, incident electron energies, and substrates. The parameters were found to agree with other parameters that can be physically correlated with electron-scattering processes and with available experimental data. These approximations and parameters provide quantitative guidelines for understanding and compensating of electron-scattering and proximity effects in electron-beam lithography.

Proximity effect in electron-beam lithography

A simple technique for the computation of the proximity effect in electron-beam lithography is presented. The calculations give results of the exposure intensity received at any given point in a pattern area using a reciprocity principle. Good agreement between the computed results and experimental data was achieved.