Electron Beam Lithography Simulation Research Articles

Comparative study of the sidewall shape and proximity effect in bilayer electron beam resist systems

The experimental investigation and simulation of electron beam lithography (EBL) for bilayer and trilayer resist systems have been carried out. Important parameters of the EBL process, such as dissolution rate, resolution, absorbed energy, and resist profile in the investigated bilayer resist systems, have been studied and discussed. Various combinations of resist layers with positive electron resist have been proposed to examine the effects of lithographic process parameters on the resist profile. The results of this work are intended for use in multilayer resist systems to produce high-frequency electronics, where the fabrication of a T-shaped gate is one of the most crucial processes.

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.

Estimation of pattern resolution using NaCl high-contrast developer by Monte Carlo simulation of electron beam lithography

The influences of different concentrations of NaCl in tetramethyl ammonium hydroxide (TMAH) developer on the electron beam lithography resolution of hydrogen silsesquioxane (HSQ) resist were studied, using original development model based on the three-dimensional (3D) energy deposition distributions (EDDs) and the experimental developing behaviors. The development behaviors of HSQ resist developed in 2.3wt.% TMAH, 2.3wt.% TMAH with 2wt.% NaCl and 2.3wt.% TMAH with 4wt.% NaCl developer were measured, respectively, to provide the solubility rates at different exposure dosages for the simulation. On the basis of the solubility rates and 3D-EDDs, the optimal EDD regions were determined for achieving sharp nanodot patterns. The optimal resist profiles of the three different developers were compared, showing that the 2.3wt.% TMAH with 4wt.% NaCl developer is suitable to form 7-nm-sized, 15-nm-pitched nanodots with sufficient height. The simulations were demonstrated to be useful for estimating the pattern resolutions with different solubility rates of developers, especially for sub-10nm nanodot fabrication.

Density multiplication of nanostructures fabricated by ultralow voltage electron beam lithography using PMMA as positive- and negative-tone resist

The authors report a density multiplication process for nanoscale patterns composed of dots and lines using electron beam lithography with low voltage 1 keV exposures and cold development. The density doubling is achieved in a single exposure-development step using polymethylmethacrylate (PMMA) as the resist. PMMA exhibits a dual positive- and negative-tone behavior depending on the electron dose employed in this density multiplication process. Fabricated nanostructures are characterized via scanning electron microscopy and subsequent feature size measurements. After density doubling, the minimum dot diameter of an initially 80 nm pitch array of single pixel dots was measured as approximately 27 nm, and the minimum width in an initially 100 nm pitch array of lines was approximately 21 nm. Methodologies for controlling the dimensions of fabricated structures are discussed. Modeling of the electron beam exposure has been carried out using an original electron beam lithography simulator in order to understand the nominal yields of scission in PMMA required in order to achieve the density multiplication, and the results are discussed.

Simulation of electron beam lithography of nanostructures

The authors report a numeric simulation tool that they developed for the modeling and analysis of electron beam lithography (EBL) of nanostructures employing a popular positive tone resist polymethylmethacrylate (PMMA). Modeling and process design for EBL fabrication of 5–50 nm PMMA structures on solid substrates is the target purpose of the simulator. The simulator is functional for exposure energies from 1 to 50 keV with arbitrary writing geometries. The authors employ a suite of kinetic models for the traveling of primary, secondary, and backscattered electrons in the resist, compute three-dimensional (3D) distributions of the yield of main-chain scission in PMMA, and convert these into the local volume fractions of fragments of various sizes. The kinetic process of development is described by the movement of the resist-developer interface with the rate derived from the mean-field theory of polymer diffusion. The EBL simulator allows the computation of detailed 3D distributions of the yield of main-chain scission in PMMA for various conditions of exposure, the corresponding volume fractions of small fragments, and the clearance profiles as functions of the development in time and temperature. This article describes the models employed to simulate the EBL exposure and development, reports examples of the computations, and presents comparisons of the predicted development profiles with experimental cross-sectional resist profiles in dense gratings.

Nanomachining and clamping point optimization of silicon carbon nitride resonators using low voltage electron beam lithography and cold development

The authors report the nanomachining of sub-20-nm wide doubly clamped silicon carbon nitride resonators using low keV electron beam lithography with polymethyl methacrylate resist and cold development. Methodologies are developed for precisely controlling the resonator widths in the ultranarrow regime of 11–20 nm. Resonators with lengths of 1–20 μm and widths of 16–280 nm are characterized at room temperature in vacuum using piezoelectric actuation and optical interferometry. Clamping and surface losses are identified as the dominant energy loss mechanisms for a range of resonator widths. The resonator clamping points are optimized using an original electron beam lithography simulator. Various alternative clamping point designs are also modeled and fabricated in order to reduce the clamping losses.

Electron Beam Lithography Simulation for the Patterning of Extreme Ultraviolet Masks

Extreme ultraviolet lithography (EUVL) mask is a complex multilayer stack, fabricated with electron-beam lithography. Detailed understanding of the scattering events and energy loss mechanism of the electron beam within this stack is mandatory due to the high accuracy requirements of the fabrication process. Simulation of electron-beam lithography is performed incorporating the details of the mask material-stack and the metrological information of the final layout is quantified. The effect of the Mo–Si multilayer of the EUVL mask blank on the deposited energy in the resist film is investigated. Simulation of complex layout containing features of various sizes down to 100 nm reproduced experimental metrology trends on the fine features of the layout.

Monte Carlo Simulation of Projection Electron Beam Lithography

We have calculated angular and energy loss distributions of electrons transmitted through masks for electron projection lithography by using a Monte Carlo simulation method. The angular and energy loss distributions are much wider in the mask stack than those in the membrane layer. The large non-scattering and non-energy-loss probabilities are also found for the membrane layer. High contrast image can thus be achieved within a small size of aperture.

Electron-beam lithography simulation for the fabrication of EUV masks

EUV lithography is considered as a possible technology for the mass production of devices at the 32 nm technology node and beyond. One special characteristic of EUV masks is its composition (Mo/Si multilayer, absorbing layer, etc.) which is totally different for the conventional photomask. This has to be considered explicitly in the simulation of electron-beam energy dissipation calculation (EDF(r)) using Monte Carlo methods. So far the application of analytical methods is very difficult in the case of substrates more complex than resist/layer, 1/layer, 2/bulk layer. The Monte Carlo procedure is utilized for the electron-beam energy deposition in a resist film covering a multi-layer of Mo/Si layers on top of a Si substrate. The effect of the number of layers of the Mo/Si structure and their thickness in terms of incident electron energy, on the backscattering coefficient and on the deposited energy in the multilayer stack is investigated.

低露光量電子ビームリソグラフィにおけるレジストパターンエッジラフネスへの電子散乱の影響

Electron beam lithography simulation is presented. A line pattern edge roughness of a resist after development process is discussed based on simulations of electron scattering in the resist film and the resist development process. Fixed threshold energy model is applied for the simulation and variations of a line width and the line edge roughness are obtained as functions of the incident electron energy, resist thickness and electron doses. The minimum line edge roughness is obtained, when the dose is more than that can be produced just the designed width of lines. As the dose increases more than that to obtain the minimum edge roughness, the roughness increases with increasing the dose. On the contrary, the roughness decreases with the dose as the statistical nature at very large doses as 100μC/cm2. Variable threshold energy model is applied and a dose variation of the line edge roughness is obtained. The LER is just reproduced by the statistical fluctuation, and it shows a linear relationship with 1/√dose Although the results obtained by present analyses agree qualitatively with experiments, the edge roughness obtained by experiment shows much smaller than the results, and some other mechanisms should be taken into account for the quantitative agreement.

Dependence of linewidth and its edge roughness on electron beam exposure dose

Electron beam lithography simulation is presented. A line pattern edge roughness of a resist after development process is discussed based on simulations of electron scattering in the resist film and the resist development process. Fixed threshold energy model is applied for the simulation and variations of linewidth and the line edge roughness are obtained as functions of the incident electron energy, resist thickness, and electron doses. The energy range calculated is from 1to5keV, the resist thickness ranges from 20to70nm, and the electron dose ranges from 1to100μC∕cm2. The resist assumed is poly(methylmethacrylate) and the film is on a Si substrate. In the present study, the threshold energy density is determined as 1.44×1021(eV∕cm3) to draw a given linewidth of 100nm, then the value of the line edge roughness is obtained. The minimum line edge roughness is obtained when the dose is more than that to produce the designed linewidth. As the dose is increased more than that to obtain the minimum edge roughness, the roughness increases with increasing the dose. For very large doses the roughness decreases with the dose, as it is explained by the statistical characteristics.

Electron-beam lithography simulation for EUV mask applications

Extreme-ultraviolet-(EUV) mask fabrication using electron-beam lithography has to eliminate the proximity effect defects, for the accurate representation of the patterned features. One special characteristic of EUV masks is that they contain a multilayer stack of repeated Si/Mo thin layers. This has to be considered explicitly in the simulation of electron-beam energy dissipation calculation using Monte Carlo methods. In a first approximation to the problem of electron scattering in a multi-layer substrate, the continuous slowing down approximation utilizing the Rutherford differential cross section is used in order to describe the electron inelastic energy loss mechanism and determine the amount of deposited backscattered energy, in the resist film on top of the multi-layer substrate. Three-dimensional modeling is used and in this first attempt to describe the process, no secondary electron generation or other excitation processes are considered. The effect of the number of layers and their relative thickness in terms of incident electron energy is investigated.

Analysis of Fitness Functions for Electron-Beam Lithography Simulation and Evolutionary Optimization

In a previous paper, an electron-beam lithography simulation and optimization tool based on a genetic algorithm was presented. The fitness function was defined as the inverse value of the Euclidian distance between a resampled computed resist profile and its targeted counterpart. In this letter, this previously proposed fitness function is analyzed and its limitations are presented. It is shown that due to out-of sync effects, the fracas function is intrinsically flawed and is not well-defined for small in. dentations in the mist profile and/or a large number of nodes along the resampled chain. An alternative fitness function based on the computation of the enclosed area between the calculated resist profile and the targeted one is proposed. It is shown-both theoretically and experimentally-that this function is able to remove the small indentations that previously appeared in the optimized resist profile. This improvement has a direct impact on the quality of the fabricated structures.

Electron beam lithography simulation for sub-quarter-micron patterns on superconductingsubstrates

High temperature superconducting (HTS) devices offer significant performance (highersignal to noise ratio, sensitivity etc) improvement over conventional devices, becoming moreprominent when device dimensions are scaled down. A typical technology for thefabrication of devices with very small critical dimensions is electron beam lithography. Inthe current work, a detailed study of the electron beam lithography process ispresented using two simulation methods: one based on Monte Carlo simulation andone based on the Boltzmann transport equation. Simulation energy depositionresults are compared with experimental ones in the case of Si and superconductingsubstrates for the first time, with satisfactory agreement found. The experimentaldata for statistical distributions of the scattered electrons were calculated in thecase of an epoxy based chemically amplified resist film deposited on Si and onY Ba2Cu3O7−δ/SrTiO3. The substrate strongly influences the distribution of the backscattered electrons due to thedifferent effective atomic number and the mass densities of the substrate and YBCO layer arestudied. It is shown that the decrease of the effective atomic numbers of the substrates (MgO andSrTiO3 in comparison with YBCO) leads to an increase in the external proximityeffect obtained in regions far from the point of beam incidence on the resist(2 µm for 25 keVand 10–11 µm for 75 keV in the case of MgO). On MgO andSrTiO3 substrates the proximity effect is lower than on YBCO substrate (bulk YBCO) in regionsnear to the point of beam incidence. Using simulation tools, accurate prediction offinal resist profiles (after development) over a wide exposure dose range of densesub-quarter-micron structures is performed for both Si and superconducting substrates.

Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms

Genetic and simplex-downhill (SD) algorithms were used for the optimization of the electron-beam lithography (EBL) step in the fabrication of microwave electronic circuits. The definition of submicrometer structures involves complex exposure patterns that are cumbersome to determine experimentally and very difficult to optimize with linear search algorithms due to the high dimensionality of the search space. An SD algorithm was first used to solve the optimization problem. The large number of parameters and the complex topology of the search space proved too difficult for this algorithm, which could not yield satisfactory patterns. A hybrid approach using genetic algorithms (GAs) for global search, and an SD algorithm for further local optimization, was unable to drastically improve the structures optimized with GAs alone. A carefully studied fitness function was used. It contains mechanisms for reduced dependence on process tolerances. Several methods were studied for the selection, crossover, mutation, and reinsertion operators. The GA was used to predict scanning patterns for 100-nm T-gates and gate profiles with asymmetric recess and the structures were fabricated successfully. The simulation and optimization tool can help shorten response times to alterations of the EBL process by suppressing time-consuming experimental trial-and-error steps.

Improvement in partitioning method for electron beam lithography simulation

We propose an improved method to calculate the energy deposited in resist for electron beam lithography simulation. The concept of the method is that an exposure intensity distribution (EID) function is partitioned into rings having a constant contribution. The equi-contribution partitioning (ECOP) method decreases the partitioning ring number for the expression of EID and the calculation time dramatically. Using the experimental result of the EID at an acceleration voltage of 100 kV for various patterns, the ECOP method was evaluated for calculation accuracy and calculation time. The time required in this method with a ring number of 50 is ten times shorter than that in the conventional method with the number of rings over 600 while the accuracy obtained by this method is better than that by the conventional method.

Application of the partial wave expansion method in 3-D low energy electron beam lithography simulation

In this paper, the partial wave expansion method (PWEM) is used in order to calculate the electron elastic scattering cross section in the case of low energy electron beam lithography. The cross section was evaluated by a numerical approach and introduced into the main Monte-Carlo program as a look-up table in order to reduce simulation time. The results are compared to the Born approximation in the case of PMMA and a polyoxometalate resist. The results are incorporated into the SELID simulator in order to obtain the final developed profiles. It was deduced that the PWEM is necessary for low energies and high-Z substrates.

Electron beam lithography simulation for high resolution and high-density patterns

A fast simulator for electron beam lithography, called SELID TM, is applied for the simulation and prediction of the resist profile of high-resolution patterns in the case of homogeneous and multilayer substrates. For exposure simulation, an analytical solution based on the Boltzmann transport equation (where all important scattering phenomena have been taken into account) for a wide range of e-beam energies is used. The case of substrates consisting of more than one layer (multilayer) is considered in depth as it is of great importance in e-beam patterning. By combining the energy deposition data from simulation with analytical functions describing the resist development (for the conventional positive-resist PMMA), complete simulation of dense layouts in the sub-quarter-micron range has been carried out. Additionally, the simulation results are compared with experimental ones for dense patterns in the sub-quarter-micron region. By using SELID TM, forecast of resist profile with considerable accuracy for a wide range of resists, substrates and energies is possible, reducing in that way the cost of process development. Additionally, proximity effect parameters are extracted easily for use in any proximity correction package.

System for measurement of the development parameters of electron beam resists

AbstractThe accuracy of profile simulation calculations depends heavily on the accuracy of the parameters used. In particular, the development parameters, which represent the development characteristics (profile and sensitivity) of the resist, have a significant effect on profile simulation accuracy. However, as yet there have been almost no studies into methods used to calculate the development parameters for electron beam lithography, nor have there been comparisons of simulation results using these development parameters with observed resist profiles. In light of this, the authors have developed a system for the measurement of development parameters for use in simulations of electron beam lithography, and have undertaken study into the methods used to calculate such development parameters. In addition, the authors have also attempted to compare simulation results with observed resist profiles. Specifically, a diazanaphthoquinone–novolac resin positive‐type electron beam resist and a chemically amplified positive‐type electron beam resist were used, to which the Fujino development rate equation and the Mack development rate equation were applied. Trial calculations of the development parameters were performed, and the parameters thus obtained were input into a ProBEAM/3D electron beam lithography simulator. The electron beam resist profiles were simulated and compared with SEM images of actual resist samples. From the results it was found that both the Fujino and Mack development rate equations accurately reproduce resist behavior for the novolac positive‐type electron beam resist, whereas the Mack development rate equation was more accurate than the Fujino equation for the chemically amplified positive‐type electron beam resist. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(4): 16–25, 2001

Evolutionary optimization of the electron-beam lithography process for gate fabrication of high electron mobility transistors

An electron-beam lithography simulation tool was realized. This tool models the development of multilayered poly(methylmethacrylate) resist structures after exposure with an electron beam. A development front propagates inside the resist stack as a function of time and the local solubility. The local solubility was experimentally measured versus the electron dose for different types of resist. The efficiency of incident and backscattered electrons was determined using doughnut-shaped structures. The ratio of the backscattered to incident electron efficiencies η was found to be 1.35 for an acceleration voltage of 30 kV on InP substrates. We used genetic algorithms to optimize the electron dose necessary for the realization of a given resist profile. This tool was applied to fabricate T-gates and asymmetric gate recesses.