Proximity Effect Correction Algorithm Research Articles

Fast and accurate proximity effect correction algorithm based on pattern edge shape adjustment for electron beam lithography

This paper proposes a fast and accurate shape-based proximity effect correction (PEC) algorithm based on pattern edge shape adjustment (PESA) for electron beam lithography (EBL). By performing PEC calculations with three layout sizes (1 μm, 2 μm, and 4 μm) under three technology nodes (40 nm, 28 nm, and 14 nm), it is shown that the proposed PESA algorithm runs about 3–10 times faster than the traditional shape-based algorithm given that the mean square error (MSE) is less than 1%. The PESA's speed advantage is more obvious in more advanced technology node. Besides, PESA helps preventing fatal misconnection between local patterns in IC layouts. High stability and robustness of PESA algorithm are also demonstrated by the excellent convergence characteristics under different process critical dimensions (CD) and layout sizes. The proposed PESA algorithm has been integrated into the electronic design automation (EDA) tool for EBL -- “HNU-EBL” which is freely available at http://www.ebeam.com.cn.

Isofocal dose based proximity effect correction tolerance to the effective process blur

The isofocal dose in electron beam lithography (EBL) is defined as the dose that results in the same feature size independent of the effective blur (blureff), which is the result of a combination of resist processing, spot size, beam focus, forward scattering, etc., that contributes to the final resist image. In other words, as blureff changes the same feature size is still obtained while using the same dose. This phenomenon is clearly demonstrated in EBL simulation when varying the blureff. In this work, the authors identify the isofocal dose for a given resist process consisting of 200 nm of ZEP520A from ZEON Chemicals atop a Si substrate using 300 nm line-space tower patterns with pattern densities ranging from 0% to 100% on an Elionix ELS-7500EX 50 keV EBL tool with a fixed 20 MHz clock at 200 pA with a 30 μm final aperture and a 20 nm beam step size. In this experiment, the dominant component of the blureff is the electron beam focus. By comparing line width measurements from tower patterns exposed with a focused beam with those from a defocused beam, the resulting blureff manifest themselves in the exposure latitude as a change in slope for each pattern density. Superimposing the exposure latitudes from each blureff at their specific pattern density, the intersection of said curves indicates the pattern density dependent isofocal dose of the resist process. Despite the difference in the blureff, the response to the correction remains invariant when the density dependent isofocal doses are aligned properly using a tunable proximity effect correction (PEC) algorithm. This means if a PEC yields the appropriate pattern density dependent isofocal doses, the same feature sizes will be consistently attainable across all pattern densities regardless of the beam focus accuracy. The text that follows demonstrates the technique used to empirically identify the pattern density isofocal doses for a given resist processes and its application using a commercially available PEC algorithm.

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.

Proximity-effect correction for 3D single-photon optical lithography.

A proximity-effect-correction (PEC) algorithm for three-dimensional (3D) single-photon gray-scale photolithography is proposed and numerically analyzed in this paper. The gray-scale dose assigned to every point within the photoresist volume is optimized to guarantee that the fabricated 3D patterns are as close to the designed patterns as possible. PEC optimizations for 3D woodpile geometries using low and high absorption photoresist are simulated. Spatial resolution of the proposed PEC algorithm is numerically studied. We also investigated the efficacy of our algorithm on a variety of related 3D geometries.

Variation of backscatter electron intensity

The authors report experimental data on the dose contribution of backscattered electrons on a silicon substrate. The backscattered electron intensity, i.e., the relative dose contribution from backscattered electrons with respect to direct write dose, is not constant, but varies with the percentage of the total dose received by backscattered electrons. In order to measure the backscattered electron contribution, the position and number of electrons are controlled by electron beam lithography. The dose contribution is measured using a negative electron beam resist, which quantifies the electron interactions in a nanoscale volume on the surface of the substrate. The data presented here will lead to improvements in proximity effect correction algorithms and ultimately improve pattern creation using electron beam lithography.

Experimental optimization of the electron-beam proximity effect forward scattering parameter

The electron-beam forward scattering parameter α characterizes the width of the incident beam plus an additional radius due to scattering of primary electrons in the resist. These “forward scattering” effects can be included in proximity-effect correction algorithms by using the point-spread energy function generated by a Monte Carlo simulation. Alternatively, correction algorithms may use a superposition of Gaussian functions to fit Monte Carlo simulations or to fit experimental data. Long-range (β>10μm) effects due to electrons backscattered from the substrate are well characterized by simulations; however, forward scattering effects are difficult to model or measure. Experimental methods of measuring α include the exposure of dot arrays, line arrays, or so-called “doughnut” patterns over a large range of doses. Proximity parameters are then inferred indirectly through fitting line and dot widths. We have instead used a simpler and faster technique based on the method of [Dubonos et al., Microelectron. Eng. 21, 293 (1993)] which uses a liftoff technique to choose the optimal value of the forward scattering parameter α. We have applied this technique to determine α for 100 kV exposure of poly(methyl methacrylate) and KRS resists. Negative resist presents more of a challenge, and so a method of optimizing α for negative resists is presented. This work includes the variation of α as a function of resist thickness, and compares these values to those inferred from Monte Carlo simulations. We also discuss the dependence of α on resist developer and the effects of distortions from the developer meniscus.

Monte-Carlo-Based Automatic Design of Chromeless Phase Shift Mask

The optical proximity effect correction algorithm (OPERA) program based on the Monte-Carlo method has been used for optical proximity correction (OPC) and phase shift mask (PSM) generation for low-NA projection lithography systems. To apply OPERA to high-NA systems, we adopted an imaging model based on a vector diffraction theory. Also, we developed a new convergence algorithm that does not reduce the degree of freedom and prevents the convergence process from falling into a local minimum. The new program, OPERA-V, is at least 10 times faster than the previous version. OPERA-V not only improves the computation time of traditional OPC, but can also be used as an automatic design tool for creating chromeless PSMs.

Proximity effect correction using pattern shape modification and area density map for electron-beam projection lithography

A novel proximity effect correction algorithm using pattern shape modification and the area density map method for electron-beam projection lithography is proposed. This algorithm enables fast, accurate and self-consistent calculation of modified pattern sizes. The correctable minimum feature sizes for shape modification were investigated from two viewpoints, mask fabrication restriction and dose margin. The correctable minimum sizes are mostly determined by the dose margin requirement in the case of isolated and dense repeated patterns, implying that the tool resolution determines correctable minimum sizes. A special technique is required for isolated space patterns where the backscattering energy cannot be reduced by simple sizing. We have implemented an algorithm in which pattern densities at middle parts of large patterns are reduced by using a lines and spaces (L/S) pattern or mesh patterns for that case. Successful correction results down to 60 nm from the simulation and 100 nm from the experiment have been obtained.

Accuracy and efficiency in electron beam proximity effect correction

We present a suite of electron beam proximity effect correction algorithms which incorporate elements of various shape-to-shape techniques as well as field-based techniques. They are applied to a set of prototypical pattern data at simulated electron beam exposure conditions ranging from 25 to 100 keV on bulk substrates. The results are compared in terms of correction accuracy and computational efficiency. In addition, we show how these algorithms, when used in combination with one another, can be applied to hierarchical pattern design data such that the correction can be obtained with a high degree of accuracy without requiring unnesting of the hierarchy.

A Monte Carlo study of proximity effects in electron-beam patterning of high- Tc superconducting thin films

In the present work the proximity effects during the electron-beam lithography of YBa 2Cu 3O 7 high temperature superconducting thin films deposited on two typical substrates (SrTiO 3 and MgO) were studied at various beam voltages (25, 50, and 75 kV) by means of the Monte Carlo simulation. The radial distributions of the absorbed electron energy density obtained for all possible sets of initial conditions were approximated by an analytical function (namely a combination of a double Gaussian and an exponential function) and the parameters of this function were calculated. The distributions obtained in the present work as well as the calculated parameters of the so-called “proximity function” can be used in a proper proximity effect correction algorithm as well as in a profile development model.

Monte Carlo simulation of electron-beam exposure distributions in the resist on structures with high-T c superconducting thin films

The spatial distributions of absorbed electron energy density in PMMA on structures incorporating YBa 2Cu 3O 7 high- T c superconducting thin films deposited on different substrates were determined using a Monte Carlo simulation (MCS), which takes into account the exact boundary conditions on interfaces between different layers of the target. The ability of our Monte Carlo program to accurately simulate the radial exposure distributions was demonstrated. The effects of substrate material (SrTiO 3 and MgO), beam energy (40 and 80 × 10 −16J) and high-temperature superconducting (HTS) film thickness (100 and 300 nm) on these distributions were investigated. The distributions obtained in this work can further be employed in a proximity effect correction algorithm as well as in a proper development model.

Energy density function determination in very-high-resolution electron-beam lithography

A proximity effect correction algorithm requires an accurate knowledge of the energy density function (EDF) deposited in the electron resist layer. In case of high-resolution electron-beam lithography (EBL), whenever the required resolution is below 0.5 μm, forward and large-angle backward scattering contribution has to be carefully analyzed. In this paper, we compare Monte Carlo (MC) simulation data with experimental point exposure measurements over different substrates and with different beam energy (range 20–40 kV). The substrates we analyze are silicon and silicon nitride membranes (2 μm thick), indium phosphide, and gold. A good correlation between MC data and experiments is proved. Experiments and MC data suggest that the usual double Gaussian fit applied to the distribution is not suitable for the application of high-resolution lithography or with high-Z materials. These data indicate that the recently proposed triple Gaussian fit can be considered as a particular case of a more complex multi Gaussian function. Experimental high-resolution resist profiles are then simulated successfully using MC EDFs in a cell development model.

Proximity effect correction using a dose compensation curve

A new concept, the dose compensation curve, is described for use in a proximity effect correction algorithm. The dose compensation curve links dose compensation factors, developed resist images, and calculated values of energy density at pattern boundaries. An experimentally measured dose compensation curve agrees very well with theoretical predictions. This technique has been successfully implemented in a fast promixity-effect correction algorithm which automatically corrects the exposure dose factor in the electron-beam data base for vector scan machines.