Exploring the fundamental limit of CD control: a model for shot noise in lithography

Yu, Ming L.; Sagle, A.; Buller, Benny

doi:10.1117/12.613661

Cited by 11 publications

(15 citation statements)

References 12 publications

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“…Here we are going to present its salient features and discusses the relation to lithographic parameter. A detailed derivation of the model will be reported in another publication 11 . There have been several attempts to model shot noise effects using both Monte Carlo simulations 9,10 and analytic approaches [6][7][8] .…”

Section: Phenomenlogical Model and Comparison With Experimentsmentioning

confidence: 99%

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Exploring the fundamental limit of CD control: a measurement of shot noise induced CDU in e-beam lithography

Sagle

Buller

2005

SPIE Proceedings

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We have used our Quadra lithography system to evaluate the shot-noise-induced critical dimension uniformity (CDU). We found that at the isofocal dose, the shot-noise-induced CDU is directly proportional to the edge blur, and hence the rate of CD changes with dose. This emphasizes the importance of minimizing beam blur of the system. We used a phenomenological model to analyze our experimental data. The model included the counting statistics of the incident electrons and that of the electron induced chemistry. With the proper parameters, this model matches the experimental observations well. It also predicts the limit of the improvements and suggests guides for the optimization of the lithographic process.

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Section: Phenomenlogical Model and Comparison With Experimentsmentioning

confidence: 99%

“…In the linewidth direction, it is averaged by the resist smoothing length R defined above. The resultant shot noise induced 3σ CDU for an isolated line (c = 0) can be shown 11 …”

Section: Phenomenlogical Model and Comparison With Experimentsmentioning

confidence: 99%

Exploring the fundamental limit of CD control: a measurement of shot noise induced CDU in e-beam lithography

Sagle

Buller

2005

SPIE Proceedings

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“…This behavior is also observed by Yu et al (2005). In the case of nonchemically amplified resists, the range of the secondary electrons d se ෂ 5 nm instead of d r will add to the total spot size.…”

Section: Shot-noise Effect On Line-width Control In Lithographymentioning

confidence: 50%

Shot noise in electron‐beam lithography and line‐width measurements

Kruit

Steenbrink

2006

Scanning

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Electron-beam lithography is used extensively in nanoscience and technology for making masks for the semiconductor industry and, on a limited scale, for maskless lithography: that is, writing the patterns directly on the chip. We expect the latter application to extend in the years to come. Control of the dimensions of the written structures is essential in the semiconductor industry. For 45 nm generation, which is presently under development and should reach production at the end of the decade, the required control over the line width is between 1.5 and 5 nm, depending on the application. One of the factors of influence on the line-width control is the statistics in the number of electrons illuminating the resist. This effect gives line edge roughness, or in other words a lack of control over the local position of a resist edge. This has long been recognized and often discussed. Recently, we developed an analytic model for the line edge position variation, which we shall illustrate and expand in this paper. The model, supported by Monte Carlo simulations, demonstrates that the line-width variation is inversely proportional to the dose used for the illumination of the resist. This makes it impossible to increase the lithography throughput by developing ultrasensitive resists. For 45 nm features written with a typical resolution of 30 nm, a 30 microC/cm2 resist gives 3 nm line-width variation over line segments of 45 nm long. The line width is usually measured in an adapted critical dimension scanning electron microscope (CD-SEM). This measurement needs to be more precise than the result of the lithography step, so the requirements are typically sub-nm. Apart from all the problems to avoid systematic errors, this measurement also suffers from statistical variations, resulting from the finite number of electrons used for the measurement. In this paper we shall derive an estimate for that variation with a similar model as used for the shot noise effect in the lithography step. One of the conclusions is that for the most precise measurements of the line width it is not advisable to tune the CD-SEM for the best resolution. It is better to allow a larger probe size of the electron beam because that can be accompanied by a much larger current and thus a decrease in the noise level.

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“…Thus, it should be under strict control to achieve the best exposure uniformity and stability [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

A real-time exposure dose control algorithm for DUV excimer lasers

Liu

Qin

2008

Front. Optoelectron. China

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A real-time exposure dose control algorithm for deep ultraviolet (DUV) excimer lasers in a step-andscan optical lithography is presented. By establishing an abstract scan exposure model and analyzing the pulse-topulse energy fluctuation characteristics of DUV excimer lasers, a real-time dose regulation is implemented based on closed-loop feedback control, which especially focuses on reducing the effect of pulse energy overshot and pulseto-pulse stochastic fluctuation. The experiment conducted on an ArF excimer laser with wavelength of 193 nm, repetition rate of 4 kHz, and pulse energy of 5 mJ confirms that such a real-time dose control algorithm is able to achieve a dose accuracy of above 0.89% even with only 20 pulses. It is fully expected that this algorithm will not only meet increasingly stringent dose accuracy requirements for sub-half-micron lithography, but also be helpful to improve lithography throughput as well as efficiency.

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Exploring the fundamental limit of CD control: a model for shot noise in lithography

Cited by 11 publications

References 12 publications

Exploring the fundamental limit of CD control: a measurement of shot noise induced CDU in e-beam lithography

Exploring the fundamental limit of CD control: a measurement of shot noise induced CDU in e-beam lithography

Shot noise in electron‐beam lithography and line‐width measurements

A real-time exposure dose control algorithm for DUV excimer lasers

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