Analysis of UV radiation transport in polymers exhibiting one-photon incubated absorption

Abstract

Abstract. An analytical solution of the radiation transport equation for polymers that exhibit a one-photon induced permanent increase in their absorption coefficient (incubated absorption) is presented. Expressions describing the small-signal and finite pulse-energy (i.e., laser pulse) transmission, and the spatio-temporal development of the absorption coefficient are derived at both the irradiating and other wavelengths for samples of arbitrary optical density. The results are found to provide a good description of experimental results for transmission in the subablation threshold regime in appropriate systems, e.g., polymethylmethacrylate irradiated using the 248 nm KrF laser and low-density polyethylene irradiated using the 193 nm ArF laser. 81.60.Jw, 81.40.Tv It is well known that the exposure of certain organic polymers to pulsed UV lasers or continuous UV lamp sources can lead to a growth in their UV absorption as a result of the introduction of new chromophores by photochemical reactions [1][2][3][4][5][6]. These chromophores can increase absorption not only at the irradiating wavelength )~o but also at other wavelengths (usually on the long-wavelength side of 2 o), where the unirradiated polymer is essentially transparent. In UV laser experiments on relatively weakly absorbing polymers this steady growth in absorption can explain why there is a delay, in terms of number of pulses, before ablation commences, i.e., a so called incubation effect [1][2][3]. In these systems it has also been demonstrated that "incubated" absorption induced by short wavelength exposure can permit the subsequent ablation of the polymer at a longer laser wavelength and at a significantly lower fluence than tbr the unexposed case [3]. Low fluence pattern definition followed by maskless high fluence laser exposure is possible, reducing mask damage problems [7].An analysis of radiation transport in polymers or similar systems which exhibit a significant incubation effect is complicated by the fact that the absorption coefficient exhibits a spatio-temporal dependence. Numerical solutions for various multiphoton processes have been reported [2,8] and used to discuss ablation phenomena for nanosecond and ultrashort excimer laser pulses. Here we present an analytical solution of the photon transport equation for systems irradiated below the threshold fluence for ablation in which single-photon incubation is dominant. The expressions derived are used to analyse the irradiance and fluence transmission for samples of arbitrary optical density and compared with available experimental results. Although the analysis is restricted to low photochemical conversion (i.e., saturation of incubation is neglected) the results are found to provide a good description of the behaviour of appropriate systems (e.g., PolyMethylMethAcrylate PMMA and polyethylene) over a useful range of conditions. TheoryWe consider a system in which one-photon induced chemical modification by radiation at wavelength 20 transforms chromophores existing at a density no a...

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“…3 that the incubation period can be observed at lower fluences where more laser pulses may be needed in order to reach the ablation threshold. This effect has also been observed and reported for polymers by other investigators 20,21 . To avoid possible errors in the assessment and evaluation of the interaction process, a distinction must be made between the actual physical ablation and non-linear surface roughness (i.e.…”

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“…7 that "Incubation" effect or period can be observed at lower fluences where more laser pulses may be needed in order to reach the ablation threshold. It may be worth while to notice that this effect had also been observed and reported for polymers by other investigators [Srinivassan et al, 1990;Dyer & Karnakis, 1994]. Also to avoid possible errors in assessment and evaluation of interaction process a distinction must be made between the actual physical ablation and surface non-linear roughness (ie.…”

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“…This effect is most pronounced in the irradiation of films that absorb weakly at the irradiation wavelength (e.g., CH 2 Cl 2 and C 6 H 12 at 248 nm), 168 but it is also observed 38,167 for compounds such as C 6 H 5 Cl, in that their photolysis results in products that are stronger chromophores than the precursor. The observation of incubation even for the simple van der Waals films clearly shows that, in the corresponding phenomenon in polymers, 1,11,170,171 the necessity of chain breakage is of minor importance for its observation. Analytical modeling of the optical changes effected to the substrate with successive laser pulses has been described in ref 171.…”

“…The observation of incubation even for the simple van der Waals films clearly shows that, in the corresponding phenomenon in polymers, 1,11,170,171 the necessity of chain breakage is of minor importance for its observation. Analytical modeling of the optical changes effected to the substrate with successive laser pulses has been described in ref 171.…”