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

Abstract

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.

Thermal conductivity in disordered porous nanomembranes

“…Here in order to fabricate the disordered structures we have modified the fabrication process based on electron beam lithography (EBL) and reactive ion etching (RIE) on free-standing membranes (Norcada Inc.) [9]. EBL systems are designed to be robust to external noise in order to reproduce the design with the highest accuracy and the influence of shot noise for example is reduced [10]. To intentionally introduce disorder in our structures, we recurred to a noise-assisted EBL, where strong external vibrations distort the beam path.…”

CAD/CAM for scalable nanomanufacturing: A network-based system for hybrid 3D printing

“…Representative examples are electron-/ion beam lithography and FIB milling. In lithography, a shot noise (dose fluctuation) limits a local position control of irradiated charged particles in the resist, resulting in a line edge roughness 64,65 . In FIB milling, although it can avoid the shot noise due to high ion dose during beam-matter interactions, it is difficult to forecast all nanoscale effects due to side effects such as secondary sputtering, surface swelling, material redeposition, and so on .…”

Determination of line edge roughness in low dose top-down scanning electron microscopy images

“…The method of fitting a Gaussian to an integrated SEM image is also found in Ref. 18, where it is used to estimate line widths. This study, however, considers a more complicated fit for the determination of LER.…”