Tip characterization method using multi-feature characterizer for CD-AFM.

In atomic force microscopy (AFM) metrology, the tip is a key source of uncertainty. Images taken with an AFM show a change in feature width and shape that depends on tip geometry. This geometric dilation is more pronounced when measuring features with high aspect ratios, and makes it difficult to obtain absolute dimensions. In order to accurately measure nanoscale features using an AFM, the tip dimensions should be known with a high degree of precision. We evaluate a new AFM tip characterizer, and apply it to critical dimension AFM (CD-AFM) tips used for high aspect ratio features. The characterizer is made up of comb-shaped lines and spaces, and includes a series of gratings that could be used as an integrated nanoscale length reference. We also demonstrate a simulation method that could be used to specify what range of tip sizes and shapes the characterizer can measure. Our experiments show that for non re-entrant features, the results obtained with this characterizer are consistent to 1nm with the results obtained by using widely accepted but slower methods that are common practice in CD-AFM metrology. A validation of the integrated length standard using displacement interferometry indicates a uniformity of better than 0.75%, suggesting that the sample could be used as highly accurate and SI traceable lateral scale for the whole evaluation process.

Mechanically induced silyl ester cleavage under acidic conditions investigated by AFM-based single-molecule force spectroscopy in the force-ramp mode.

AFM-based dynamic single-molecule force spectroscopy was used to stretch carboxymethylated amylose (CMA) polymers, which have been covalently tethered between a silanized glass substrate and a silanized AFM tip via acid-catalyzed ester condensation at pH 2.0. Rupture forces were measured as a function of temperature and force loading rate in the force-ramp mode. The data exhibit significant statistical scattering, which is fitted with a maximum likelihood estimation (MLE) algorithm. Bond rupture is described with a Morse potential based Arrhenius kinetics model. The fit yields a bond dissociation energy De = 35 kJ mol(-1) and an Arrhenius pre-factor A = 6.6 × 10(4) s(-1). The bond dissociation energy is consistent with previous experiments under identical conditions, where the force-clamp mode was employed. However, the bi-exponential decay kinetics, which the force-clamp results unambiguously revealed, are not evident in the force-ramp data. While it is possible to fit the force-ramp data with a bi-exponential model, the fit parameters differ from the force-clamp experiments. Overall, single-molecule force spectroscopy in the force-ramp mode yields data whose information content is more limited than force-clamp data. It may, however, still be necessary and advantageous to perform force-ramp experiments. The number of successful events is often higher in the force-ramp mode, and competing reaction pathways may make force-clamp experiments impossible.

A density functional theory model of mechanically activated silyl ester hydrolysis.

To elucidate the mechanism of the mechanically activated dissociation of chemical bonds between carboxymethylated amylose (CMA) and silane functionalized silicon dioxide, we have investigated the dissociation kinetics of the bonds connecting CMA to silicon oxide surfaces with density functional calculations including the effects of force, solvent polarizability, and pH. We have determined the activation energies, the pre-exponential factors, and the reaction rate constants of candidate reactions. The weakest bond was found to be the silyl ester bond between the silicon and the alkoxy oxygen atom. Under acidic conditions, spontaneous proton addition occurs close to the silyl ester such that neutral reactions become insignificant. Upon proton addition at the most favored position, the activation energy for bond hydrolysis becomes 31 kJ mol(-1), which agrees very well with experimental observation. Heterolytic bond scission in the protonated molecule has a much higher activation energy. The experimentally observed bi-exponential rupture kinetics can be explained by different side groups attached to the silicon atom of the silyl ester. The fact that different side groups lead to different dissociation kinetics provides an opportunity to deliberately modify and tune the kinetic parameters of mechanically activated bond dissociation of silyl esters.

Single-molecule force-clamp experiments reveal kinetics of mechanically activated silyl ester hydrolysis.

We have investigated the strength of silyl ester bonds formed between carboxymethylated amylose (CMA) molecules and silane-functionalized silicon oxide surfaces using AFM-based single-molecule force spectroscopy in the force-clamp mode. Single tethered CMA molecules were picked up, and bond lifetimes were determined at constant clamp forces of 0.8, 1.0, and 1.2 nN at seven temperatures between 295 and 320 K at pH 2.0. The results reveal biexponential rupture kinetics. To obtain the reaction rate constants for each force and temperature individually, the results were analyzed with a biexponential kinetic model using the maximum likelihood estimation (MLE) method. The force-independent kinetic and structural parameters of the underlying bond rupture mechanisms were extracted by fitting the entire data set with a parallel MLE fit procedure using the Zhurkov/Bell model and, alternatively, an Arrhenius kinetics model combined with a Morse potential as an analytic representation of the binding potential. With activation energies between 37 and 40 kJ mol(-1), and with Arrhenius prefactors between 5 × 10(4) and 2 × 10(6) s(-1), the results point to the hydrolysis of the silyl ester bond.

Mechanically activated rupture of single covalent bonds: evidence of force induced bond hydrolysis.

We have used temperature-dependent single molecule force spectroscopy to stretch covalently anchored carboxymethylated amylose (CMA) polymers attached to an amino-functionalized AFM cantilever. Using an Arrhenius kinetics model based on a Morse potential as a one-dimensional representation of covalent bonds, we have extracted kinetic and structural parameters of the bond rupture process. With 35.5 kJ mol(-1), we found a significantly smaller dissociation energy and with 9.0 × 10(2) s(-1) to 3.6 × 10(3) s(-1) also smaller Arrhenius pre-factors than expected for homolytic bond scission. One possible explanation for the severely reduced dissociation energy and Arrhenius pre-factors is the mechanically activated hydrolysis of covalent bonds. Both the carboxylic acid amide and the siloxane bond in the amino-silane surface linker are in principle prone to bond hydrolysis. Scattering, slope and curvature of the scattered data plots indicate that in fact two competing rupture mechanisms are observed.

Simple coupling chemistry linking carboxyl-containing organic molecules to silicon oxide surfaces under acidic conditions.

The coupling chemistry of carboxymethylated amylose with organo-silanized silicon oxide surfaces at pH 7.4 and 2.0 was investigated using atomic force microscopy (AFM) based single-molecule force spectroscopy. At close to neutral pH, carbodiimide activation of a carboxylic acid affords formation of an amide bond with an amino surface linker. At pH 2.0, no activation with carbodiimide was required to anchor carboxymethylated amylose between an AFM tip and a glass substrate. At the same time, the mean bond rupture force f(r) dropped from 1.65 ± 0.37 nN at pH 7.4 to 1.39 ± 0.30 nN at pH 2.0 without carbodiimide, indicating that a different link to the surface can be formed at low pH. The coupling mechanism at pH 2.0 was elucidated by a series of experiments, in which the surface was functionalized with four different organosilanes, each containing characteristic functional groups. The results are rationalized with an acid-catalyzed ester condensation between a carboxyl group and a free, unreacted silanol group in the surface anchor or on the surface.

Dynamic strength of the silicon-carbon bond observed over three decades of force-loading rates.

The mechanical strength of individual Si-C bonds was determined as a function of the applied force-loading rate by dynamic single-molecule force spectroscopy, using an atomic force microscope. The applied force-loading rates ranged from 0.5 to 267 nN/s, spanning 3 orders of magnitude. As predicted by Arrhenius kinetics models, a logarithmic increase of the bond rupture force with increasing force-loading rate was observed, with average rupture forces ranging from 1.1 nN for 0.5 nN/s to 1.8 nN for 267 nN/s. Three different theoretical models, all based on Arrhenius kinetics and analytic forms of the binding potential, were used to analyze the experimental data and to extract the parameters fmax and D(e) of the binding potential, together with the Arrhenius A-factor. All three models well reproduced the experimental data, including statistical scattering; nevertheless, the three free parameters allow so much flexibility that they cannot be extracted unambiguously from the experimental data. Successful fits with a Morse potential were achieved with fmax = 2.0-4.8 nN and D(e) = 76-87 kJ/mol, with the Arrhenius A-factor covering 2.45 x 10(-10)-3 x 10(-5) s(-1), respectively. The Morse potential parameters and A-factor taken from gas-phase density functional calculations, on the other hand, did not reproduce the experimental forces and force-loading rate dependence.