"Force-feedback" leveling of massively parallel arrays in polymer pen lithography

Abstract

Polymer pen lithography is a recently developed molecular printing technique which can produce features with diameters ranging from 80 nm to >10 microm in a single writing step using massively parallel (>10(7) pens) arrays of pyramidal, elastomeric pens. Leveling these pen arrays with respect to the surface to produce uniform features over large areas remains a considerable challenge. Here, we describe a new method for leveling the pen arrays that utilizes the force between the pen arrays and the surface to achieve leveling with a tilt of less than 0.004 degrees, thereby producing features that vary by only 50 nm over 1 cm.

Figure 1

(a) Geometric model of the tip. (b) An unleveled polymer pen array with a tilt of θ° along the y-axis and a tilt of φ° along the x-axis is brought into contact with the surface. The red pen indicates the initial point of contact with the surface.

Figure 2

The change in height for every individual pen in the polymer pen array with: (a) θ =0 and φ=0, and (b) θ =0.15° and φ=0.10°. Spacing between pens is 80 μm, and the z-piezo extension is 12 μm.

Figure 3

Total force (F_total) between the polymer pen array and the surface plotted as a function of θ and φ according to Eq. 7. The parameters for this plot are N=10000 pens, Z₀= 12 μm and L_top ,=70 nm.

Figure 4

Three-step leveling strategy for PPL. a) To level the pen array with respect to the surface, initially, θ is held constant and φ is varied until a local maximum in F_total is found. b) Subsequently θ is varied, and φ is held constant until another local maximum in F_total is found. c) Finally, θ is held constant and φ is varied again until a global maximum in F_total is found. d) By combining the plots (a–c), a 3-D plot is constructed that shows that the experimentally determined relation between the force measured by the scale beneath the substrate as a function of θ and φ agrees with the theoretically predicted curve (Figure 3).

Figure 5

The patterns made by a 10,000 pen array with (a) θ = 0, (b) θ = 0.01, and (c) θ= −0.01 °, respectively. Scale bar is 50 μm. (d) The relation between feature size and the distance to one side of the polymer pen array under different leveling conditions. (e) The diameters of different features plotted as a function of distance from one side of the pen array at different values of θ.