An Ink Transport Model for Prediction of Feature Size in Dip Pen Nanolithography

Feature size predictions in dip pen nanolithography are typically based upon the constant transport rate or the constant tip−concentration approximations. Models based upon these approximations are inaccurate due to the erroneous assumption that the diffusion of ink upon the surface and ink dissolution at the tip are independent. Herein, we explain that these two steps are related and that they share the same ink flow via the meniscus. We use this insight to generate a comprehensive ink transport model. Our model provides new insight into the (i) relative importance of tip-side transport and surface diffusion, (ii) cause of intermittent line writing at high writing speeds, and (iii) critical role of proper tip inking with respect to feature size accuracy and high-speed writing. We show that the constant rate and constant tip−concentration approaches are limiting cases of the same model, thereby unifying the two approaches and reducing errors in line width prediction by up to 30%.