PMMA development studies using various synchrotron sources and exposure conditions

2002

Fluorescence radiation during LIGA X-ray exposure and the impact of the resulting secondary dose on feature sidewall tolerances are examined using numerical methods. The study addresses fluorescence emitted by the substrate of the PMMA resist and focuses on the tolerances obtained for resists patterned with a range of feature sizes. New models of the secondary dose and subsequent feature development are presented and discussed. These models are coupled such that the evolving feature geometry during development depends on the local total dose, as well as the development temperature and the transport of PMMA fragments away from the dissolution front. We find that sidewall tolerances for typical exposure and development conditions are less than 0.1 micron for a metallized silicon substrate, but exceed several microns for thick titanium, copper and nickel substrates. We also find that these tolerances are very sensitive to the feature geometry, development temperature and the magnitude of the primary dose. IntroductionSecondary radiation is a well-known source of dimensional error in the LIGA micro-fabrication process [1][2][3][4]. During X-ray exposure of the PMMA resist, some primary photons from the synchrotron source are absorbed in the PMMA substrate. This absorption produces both highenergy photoelectrons and fluorescence X-rays. Photoelectrons emitted from the substrate are known to affect PMMA adhesion, but these are generally absorbed over a very small distance and so do not strongly affect structure accuracy. In contrast, fluorescence photons are absorbed over large distances, several millimeters in some cases. Since fluorescence is emitted isotropically, a portion of this radiation is absorbed in masked regions of the PMMA. During subsequent development, this increased dose may result in substantial dissolution of feature sidewalls, leading to dimensional errors between the patterned mask absorber and the final plastic or electroformed metal part. Secondary radiation emitted from the mask membrane may similarly contribute to sidewall dissolution and the accompanying degradation of accuracy [4].Previous computational studies of the LIGA process have addressed in some detail the two-dimensional distribution of the increased dose due to both fluorescence and photoelectrons [2][3][4][5]. However, there has been relatively little study of the effects of this distribution on the twodimensional history of development [5]. Generally, the final sidewall profile has been estimated based on contours of the total dose. This approach provides fair agreement with measured results under limited conditions, but clearly does not address the varying times each portion of the sidewall is exposed to developer. It also does not take into account that the development rate of PMMA varies smoothly with the dose down to 0.2 kJ/cm 3 or less [4].To help understand and quantify LIGA sidewall tolerances, we have developed coupled models addressing both exposure and development. The one-dimensional multiwavelength model of primary X-ra...

Section: Development Processsupporting

confidence: 86%

The influence of X-ray fluorescence on LIGA sidewall tolerances

2002

“…The constants G, B, and p are chosen as 12.3 (lm/min), 8.44 kJ/cm 3 , and 3.81 to provide a best fit to the data reported by Pantenburg et al [11] for T ¼ 21 C and for doses that span the range used in the examples treated below. These values are somewhat different than those used by Tan et al [10] to fit a data set that extends to higher doses. The activation energy is typically on the order of 140 kJ/mol, but this is of no importance to our examples as they are limited to cases with T ¼ T 0 ¼ 21 C. In a quasi-steady development process the recession rate, dh=dt, is proportional to the net dissolution rate, Rðq s À q l C b Þ, which must be in balance with the rate of fragment transport from the development surface into the bath, q l DShDC=h [12].…”

mentioning

confidence: 77%

“…Previous studies of the kinetics have shown that the dissolution rate of PMMA in a GG developer fluid may be well approximated by the expression [10].…”

mentioning

confidence: 99%

Modeling acoustic agitation for enhanced development of PMMA resists

Nilson

2002

Although acoustic agitation is known to enhance the development rate of LIGA resists, the operative physical mechanism is not well understood. Analytical and numerical models presented here suggest that the observed enhancement results from steady acoustic streaming and associated polymer fragment transport induced by the high frequency sound waves. The computed steady flow within the feature is torroidal with downflow along the feature walls and upflow in the center. The numerically calculated enhancement of fragment transport is shown to be well approximated by a closed-form expression based on a pair of asymptotic formulas for weak and strong agitation. These transport models are combined with a model of PMMA dissolution kinetics and used to predict development rates for a range of LIGA feature sizes. The results are in good agreement with experimental data from Forschungszentrum Karlsruhe.

“…The parameters a, b and c for GG developer are 13.6 lm/min, 4.6 kJ/cm 3 , and 3.8 respectively, for all synchrotron sources. Additional details of the exposure and development models have been reported previously [4,5]. These exposure and development models are coupled in a user-friendly code known as LEX-D.…”

Section: Numerical Modelmentioning

confidence: 99%

“…Kinetic-limited development rates normally depend on the development temperature and local total dose [4], but may additionally depend on the dose rate and mean photon energy of the dose. In our general development model, the kinetic rate is computed from the PMMA molecular weight after the dose.…”

Section: Numerical Modelmentioning

confidence: 99%

The influence of mask substrate thickness on exposure and development times for the LIGA process

Hruby

2000

Optimizing mask substrate thickness is an important practical concern in the X-ray exposure of PMMA resists for LIGA. An overly thick substrate necessitates long exposure times due to excessive beam ®ltering, while a substrate too thin leads to long development times due to low absorbed doses at the PMMA bottom surface. To assist in this optimization, we have developed numerical models describing both the exposure and development of a PMMA resist. These exposure and development models are coupled in a single interactive code, permitting automated adjustment of mask substrate thickness to yield the minimum of a prescribed cost object function that depends on both the exposure and development times. Results are presented for several synchrotron sources and over a wide range of the PMMA thickness. IntroductionMany factors in¯uence the design of X-ray masks used in exposing PMMA resists for the LIGA process [1, 2, 3]. One important factor is the exposure time. Overly thick mask substrates will absorb too much of the beam energy, requiring exposure times that may run to several days. Another important factor is the top-to-bottom dose ratio. Most synchrotron sources produce suf®cient low-energy photons that some ®ltering of the X-ray beam is required to obtain acceptable dose ratios in thick resists. Large topto-bottom dose ratios must generally be avoided since the top-surface dose cannot be increased without bound and low bottom-surface doses yield very long development times. A mask substrate of appropriate thickness may thus conveniently serve as the required beam ®lter. Since very thin substrates are dif®cult to manufacture, thinning the substrate and ®ltering the beam elsewhere is not desirable.To help investigate the in¯uence of mask substrate thickness on exposure and development times, we have developed coupled models of the LIGA exposure and development processes. These models are used here to parametrically study tradeoffs between exposure and development time and to directly discern the optimum substrate thickness. Sample results are presented over a wide range of the PMMA resist thickness and mask substrate thickness for exposures at the ALS (Lawrence Berkeley), SSRL (Stanford) and NSLS (Brookhaven) sources. We ®nd that tradeoffs between the exposure and development times serve to de®ne an optimum substrate thickness for each source and further identify for each source a practical limit on the maximum resist thickness. Numerical modelThe exposure model describes one-dimensional, multiwavelength X-ray transmission through an arbitrary set of ®lters, transmission through the mask absorber and substrate, and the subsequent pro®le of energy absorption through the thickness of the PMMA target. These transmission and absorption processes are modeled using wavelength-dependent transmission and absorption cross-sections. Scattering is included only as effective forward and backward scattering along the main direction of beam propagation, and elastic scattering and¯ores-cence are not yet considered. Under these res...