Reaction-diffusion analysis for one-step plasma etching and bonding of microfluidic devices

A self-similar reaction front develops in reactive ion etching when the ions penetrate channels of shallow height h. This relates to the patterning of microchannels using a single-step etching and bonding, as described by Rhee et al. [Lab Chip 5, 102 (2005)]. Experimentally, we report that the front location scales as xf∼ht1/2 and the width is time-invariant and scales as δ∼h. Mean-field reaction-diffusion theory and Knudsen diffusion give a semiquantitative understanding of these observations and allow optimization of etching times in relation to bonding requirements.