Induced nanoscale deformations in polymers using atomic force microscopy

An exact analytical solution, based on the method of images, is obtained for the description of the electric field between an atomic force microscope (AFM) tip and a thin dielectric polymer film ($30\mathrm{nm}$ thick) spin coated on a conductive substrate. Three different tip shapes are found to produce electrostatic pressure above the plasticity threshold in the polymers up to $50\mathrm{MPa}$. It is shown experimentally that a strong nonuniform electric field $(5\times {10}^8–5\times {10}^9\mathrm{V}{\mathrm{m}}^{-1})$ between the AFM tip and polymer substrate produces nanodeformations of two different kinds in planar polymer films. Nanostructures (lines and dots) $10–100\mathrm{nm}$ wide and $0.1–5\mathrm{nm}$ high are patterned in the polymer films by using two different experimental techniques. The first technique relies on electric breakdown in the film leading to polymer heating above the glass transition point followed by mass transport of softened polymer material towards the AFM tip. The second technique is believed to be associated with plastic deformation of the polymer surface at the nanoscale. In this case the nanostructures are experimentally patterned in the films with no external biasing of the AFM tip, and using only the motion of the tip. This suggests an additional nanomechanical approach for nanolithography in polymer films of arbitrary thickness.

Figure 1

(Color online) Schematic representation of the electrostatic field formation between an AFM tip and a conductive layer with a polymer film spin-coated onto the conductor. The thickness of the polymer film is $30\mathrm{nm}$. The method of images was used to determine the field (in the range of $5\times {10}^8–{10}^9\mathrm{V}{\mathrm{m}}^{-1}$), and an electrostatic pressure that deforms the polymer film. The electric charges are concentrated either on the interface $S^{\prime }$ resulting in electronic breakdown, or on the interface $S$ resulting in plastic deformation.

Figure 2

(Color online) Three different tip configurations were used to solve for the electric field distribution: (a) almost spherical tip modeled by a point charge Q; (b) parabolic tip modeled through a rare grid of the electric charges; (c) flattened tip modeled by a dense grid of the electric charges. The distance between the tip and a polymer surface was varied between 0.5 and $10\mathrm{nm}$.

Figure 3

Pressure creating deformation in a polymer film with respect to the distance in AFMEN case (charges concentrated on the interface $S^{\prime }$): (a) The electric field magnitude $\mathit{E}=4\times {10}^9\mathrm{V}{\mathrm{m}}^{-1}$, for the tip–polymer surface separation $\mathit{h}=5\mathrm{nm}$ (b) electric field magnitude $\mathit{E}=2.7\times {10}^9\mathrm{V}{\mathrm{m}}^{-1}$, for the tip–polymer surface separation $\mathit{h}=10\mathrm{nm}$; pressure vs distance for surface charges concentrated on the interface $S$; (c) the electric field magnitude $\mathit{E}=2.5\times {10}^9\mathrm{V}{\mathrm{m}}^{-1}$, for the tip–polymer surface separation $\mathit{h}=0.5\mathrm{nm}$; (d) the electric field magnitude $\mathit{E}=3.3\times {10}^9\mathrm{V}{\mathrm{m}}^{-1}$, for the tip–polymer surface separation $\mathit{h}=0.3\mathrm{nm}$; the horizontal line corresponds to the plastic deformation threshold $\mathbf{P}=25\mathrm{MPa}$. The curves (a), (b), and (c) correspond to the different AFM tip shapes presented in Fig. 2.

Figure 4

(Color online) Experimental results of the patterned nanostructures in amplitude-modulated AFMEN. Top view AFM images of (a) dots of $6\mathrm{nm}$ high and $23\mathrm{nm}$ wide patterned in polystyrene film (PS, $\epsilon =2.6$, $M_w=110\mathrm{k}$, $T_g=105°$) of $30\mathrm{nm}$ thickness. Exposure time was $1\mathrm{s}$; AFM tip bias was $-48\mathrm{V}$; average current was $10\mathrm{nA}$; (b) dot of $3\mathrm{nm}$ high inside the hole of $37\mathrm{nm}$ wide, corresponding to intermediate regime between AFMEN and ablation patterned in polymethylmethacrylate (PMMA, $\epsilon =3.2$, $M_w=960\mathrm{k}$, $T_g=115°$). Exposure time was $1\mathrm{s}$ for AFM tip bias $-26\mathrm{V}$ with average current $0.1\mu \mathrm{A}$; (c) set of holes of $4\mathrm{nm}$ deep, and $37\mathrm{nm}$ wide patterned in PMMA (ablation mode) using AFM tip bias $-30\mathrm{V}$, with exposure time $0.5\mathrm{s}$, and average current $0.5\mu \mathrm{A}$. Images (d)–(f) represent the cross section of the images (a)–(c).

Figure 5

(Color online) Experimental results of nanostructures patterned in polymer films without external bias: (a) Lines of $25\mathrm{nm}$ wide and $0.8\mathrm{nm}$ high patterned in PMMA ($\epsilon =3.2$, $M_w=528\mathrm{k}$, $T_g=115°$); AFM tip velocity was $1\mu \mathrm{m}∕\mathrm{s}$ with the average current smaller than $100\mathrm{pA}$; (b) closeup of one of the lines; (c) lines of $47\mathrm{nm}$ wide and $1\mathrm{nm}$ high patterned in PS ($\epsilon =2.6$, $M_w=110\mathrm{k}$, $T_g=105°$) without external voltage: the nanolines corresponds to lateral AFM tip motion above the surface; (d) two nanodots patterned in PMMA at the bias voltage $-13\mathrm{V}$, and $35\mathrm{nm}$ wide line with voltage turned off. AFM tip velocity was $0.1\mu {\mathrm{ms}}^{-1}$; (e) diagram of unbiased tip moving on square of $2\mu \mathrm{m}$ size above the polymer film: the tip begins moving at point 1, dwelling determined time $(0.3–2\mathrm{s})$ at each point before stops at point 9; nanoscopic dots patterned in $30\text{−}\mathrm{nm}$-thick PS film by unbiased tip for different dwelling time (f) time was $0.3\mathrm{s}$. Dot height varies between 0.5 and $1\mathrm{nm}$; (g) time was $1\mathrm{s}$. Dot height varies between 0.8 and $1.5\mathrm{nm}$; (h) time was $2\mathrm{s}$ Dot height varies between 1 and $2.4\mathrm{nm}$.