Modeling of shot noise in x-ray photoresist exposure

Turner, Scott A.; Babcock, Carl P.; Cerrina, F.

doi:10.1116/1.585819

Cited by 17 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The resist blur σ R also provides a way to smooth out the shot noise and improve the CDU as discussed when deriving Eq. (17). However, σ R also affects the edge blur as shown in Eq.…”

Section: Implications For Lithographymentioning

confidence: 94%

“…Mathematically, the relevant acid distribution is the convolution of the local dose with a smoothing function S(x). Turner et al 17 also introduced this function and they called it an "influence function". Physically it means that the development of the resist at a particular location depends on the exposure of the resist over the "smoothing width" of S(x).…”

Section: The Modelmentioning

confidence: 98%

See 1 more Smart Citation

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

Sagle

Buller

2005

SPIE Proceedings

View full text Add to dashboard Cite

We have made measurements with our Quadra raster shaped beam lithography system to evaluate the shot-noiseinduced critical dimension uniformity (CDU). We found that at the isofocal dose, the shot-noise-induced CDU is directly proportional to the edge blur, and is linear with the rate of CD change with dose. Here we propose a phenomenological model which permits an experimentalist to relate the CDU to controllable lithographic parameters. The model considers both the counting statistics of the incident electrons and the noise from the electron induced chemistry. The model suggested that the shot-noise induced CDU may be minimized by reducing the beam blur, forward scattering, through the optimization of the resist smoothing distance and maximizing the number of acid molecules created in the resist by an incident electron. With the proper parameters, this model matches the experimental observations well. It also predicts the limit of the improvements and suggests guides for future resist development. Shot-noise induced line edge roughness is also discussed.

show abstract

“…The resist blur σ R also provides a way to smooth out the shot noise and improve the CDU as discussed when deriving Eq. (17). However, σ R also affects the edge blur as shown in Eq.…”

Section: Implications For Lithographymentioning

confidence: 94%

Section: The Modelmentioning

confidence: 98%

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

Sagle

Buller

2005

SPIE Proceedings

View full text Add to dashboard Cite

show abstract

“…It has been realized that post-exposure bake (PEB) of the resist induces acid diffusion in the resist 12 . There is also the spatial burring due to a "very long catalytic chain length" in the acid-driven de-protection process 13 .…”

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

View full text Add to dashboard Cite

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.

show abstract

“…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 (Smith 1986(Smith , 1988 and often been discussed (Gallatin 2005, Henke and Torkler 1999, Kotera et al 2002, Leunissen et al 2005, Nakasugi et al 2002, Neureuther 1988, Turner et al 1991. Recently, we developed an analytical model to describe the line-edge position variation (Kruit et al 2004), which we shall illustrate and expand in this paper.…”

Section: Introductionmentioning

confidence: 88%

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

Kruit

Steenbrink

2006

Scanning

View full text Add to dashboard Cite

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.

show abstract

Modeling of shot noise in x-ray photoresist exposure

Cited by 17 publications

References 0 publications

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

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

Contact Info

Product

Resources

About