Characteristic Variation of Exposure Pattern in Cell-Projection Electron-Beam Lithography

Kotera, Masatoshi; Yamaguchi, Kazuyuki; Okagawa, Takashi; Matsuoka, Koji; Kojima, Yoshinori; Yamabe, Masaki

doi:10.1143/jjap.38.7031

Cited by 7 publications

(1 citation statement)

References 6 publications

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“…], a solid line shown as "Full beam" is obtained. by simulating all electrons existent in the beam by the ordinary Monte Carlo simulation, [5] "NN" is obtained by considering the Coulomb force between only the nearest-neighbor electrons as the stochastic Coulomb effect, "Field" is obtained by considering the beam forms a potential distribution as the global Coulomb effect, and "NN+Field" is the present result, which considers both the global and the stochastic Coulomb effects. The result of "N'' shows a short tail at the radius of 200pn1, and a small blur is found from the original beam.…”

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confidence: 99%

Calculation of Coulomb interaction among electrons in a high current electron beam exposure system

Yukumoto¹,

Kotera²

Digest of Papers Microprocesses and Nanotechnology 2003. 2003 International Microprocesses and Nanotechnology Conference

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Electron beam lithography is the most promising technology to realize the next generation LSI, but its low throughput is the most crucial issue. The simplest solution of the issue is to increase the beam current. However, as the current increases, the Coulomb interaction among electrons becomes severe, and a blur at the exposure pattem increases. In order to find the most preferable condition, it is necessary to quantify the Coulomb effect. In order to formulate the Coulomb effects, several approaches have been proposed. (l):By slicing the beam optics along the axis, the amount of the electron deviation in a segment is given by an equation. [l] (2):Considering only nearest-neighbor electron and a statistical equation is derived to express electron deviation after passing through the optics.[2] (3):Instead of deriving analytical equations, numerical treatment using Monte Carlo simulation can be flexibly applied.[3] However, since it calculates the Coulomb force between all combinations of existent electrons in the optics, as the beam current increases, the number of combination becomes large and the computation time is quite large. It is known that it is effective to reduce the calculation time by adopting a tree-code programming in high current beam, such as more than 20pA. [4] It is understood that the Coulomb interaction between electrons in the optical system can be categorized into two effects: One is the global Coulomb effect, and the other is the stochastic Coulomb effect. Electron beam in the optics produces a potential distribution as a whole, and every individual electron is influenced by the distribution as the global Coulomb effect. On the other hand, electrons in the beam may occasionally meet the other electron in a very short distance, and they will be recoiled each other, and large energy and angular deviations are found, as the stochastic Coulomb effect. In the present study we propose a new approach to consider the Coulomb effect by separating the global and the stochastic mechanisms, and then, they are combined in a Monte Carlo electron trajectory simulation. As the global Coulomb effect, the potential distribution is obtained in the beam, and the electron deflection is calculated due to the distribution. As the stochastic Coulomb effect, it is assumed that electrons interact with only their nearest-neighbor electron in the beam. All electron trajectories in the whole optical system are traced three-dimensionally considering both the potential distribution in the beam and the recoiled electron caused by the nearest neighbor electron. Since the Coulomb interaction is calculated for only one electron instead of all other electrons around the electron, the simulation time is remarkably reduced.In this model calculation, a round pattem beam with the radius of 200pm is emitted at 200" above the wafer with the energy of 2keV at 1 pA, and it is simply projected as a parallel beamThe validity of the present simulation is demonstrated in Fig.1. 112

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confidence: 99%

Calculation of Coulomb interaction among electrons in a high current electron beam exposure system

Yukumoto¹,

Kotera²

Digest of Papers Microprocesses and Nanotechnology 2003. 2003 International Microprocesses and Nanotechnology Conference

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Influence of the scattered electrons at the mask in a projection lithography system

Kotera

Ishida

Naruse

et al. 2001

Microelectronic Engineering

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Analytic evaluation of the intensity point spread function

Gallatin¹

2000

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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The intensity point spread function (PSF) for geometric imaging such as occurs in a projection electron system like SCALPEL is derived analytically from the ray aberration coefficients. The results show that, as expected, the PSF for ordinary aberrations has a finite radius and is not Gaussian. Hence blur estimates, which are often based on assuming a Gaussian PSF and computing the root-sum-square or “rss” of the separate blur radii will generally overestimate the true aberration blur. Global space charge acts like an electrostatic lens and hence its effects can be included in the PSF calculation as well. The net PSF can be convolved with an object to produce an accurate representation of the image. The convolution integral can also be performed first which yields the image intensity distribution directly in terms of the aberrations.

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Characteristic Variation of Exposure Pattern in Cell-Projection Electron-Beam Lithography

Cited by 7 publications

References 6 publications

Calculation of Coulomb interaction among electrons in a high current electron beam exposure system

Calculation of Coulomb interaction among electrons in a high current electron beam exposure system

Influence of the scattered electrons at the mask in a projection lithography system

Analytic evaluation of the intensity point spread function

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