It also includes investigations into the influence of common artifacts (such as elastic deformations and imaging multistability) and probe structure (tilt angle and number of walls in the carbon nanotube probe) on image quality. These models were used to generate accurate potential curves at different positions of the probe relative to the sample.
Results and Discussion
14 and the position (in the x-y plane) of the probe nanotube relative to the sample nanotube. The corresponding tip-sample force curve indicates that the force opposing the sliding motion of the probe was negligible.
Conclusions
In contrast, the increase in lateral resolution is due to the very localized deformation and bending of the probe nanotube along the edges of the sample nanotube and is therefore not significantly affected by vertical compression. The improvement in apparent resolution due to radial deformation of the probe nanotube in this study was a result of the relatively high driving forces applied to the AFM cantilever.
Tables of force field parameters
Ian Shapiro, Maria Esplandiu, and Patrick Collier were supported by Caltech startup funds and by Arrowhead Research. 33,34,35 Additional parameters were added to study mixed systems (containing silicon, graphitic systems, oxygen, and hydrogen) by applying arithmetic and/or geometric combination rules to existing parameters in quantum mechanical calculations by Weiqiao Deng, Richard Muller, and William A.
Energy-position and force-position curves from MD simulations
Effect of thermal vibrations
The force and energy curves presented here show that the energy requirement to pop these points is the same as the energy required to compress the probe longitudinally by one full nm, which is much greater than the available thermal energy. Our calculations show that the maximum horizontal displacement of any atom at the probe tip at 300 K is less than 0.095 nm (less than 1.8% of the probe width), which would not significantly change the relative position of probe and sample .
Characterization of SWNT deformation modes
Slipping of smaller SWNT probes: 2.2 nm diameter, 20 nm in length
Images 3–6 correspond to intermediate geometry relaxation steps of the probe and the sample after the probe is retracted. This guarantees that the probe and sample are able to relax before the tip hits the sample a second time.
Mechanisms of Single-Walled Carbon Nanotube Probe- Sample Multistability in Tapping Mode AFM Imaging *
Introduction
- Experimental
Negative values of the tip position correspond to elastic deformations in the SWNT tip and sample nanotube upon contact. Numerical integration of Equation 1 shows that in the absence of tip-specimen adhesion and frictional forces, four solutions of the oscillation amplitude are possible for the snapping mode.
Discussion
- Silicon Tips vs. SWNT Tips
- Snapping
- Importance of Adhesion and Friction
- Practical implications of multistability
This means that for pure SWNTs, for which dispersion forces are the most important interactions, most of the imaging is expected to take place in the repulsive regime. We have previously shown that snapping and sliding effects have a direct influence on the probe resolution and measured sample width.13 The results presented here show that snapping can also give rise to several solutions of the oscillating amplitude, including a continuum of solutions for large adhesion and frictional forces is present. 11,12 However, a closer analysis of the snapping potential (figure 2 (c)) and the phase curve (figure 4) reveals that the long range.
61 part of the potential results in two image solutions when the excitation force is small (too small to overcome the snap-off barrier) or the probe is sufficiently far from the sample. This indicates that either there is a significantly stronger attraction or adhesion of the SWNT tips to the surface than that corresponding to van der Waals interactions alone, or that there are other important effects that were not included in the equation of motion and magnify the effect of small van der Waals attractive forces. In our previous report13, we presented a simulation of a cross-sectional scan of a lying SWNT showing "negative" height readings in regions where the probe snapped or slipped past the sample, which does not agree with the experimental result.
The interaction of the SWNT probe with the substrate is responsible for the existence of one attractive and one repulsive amplitude solution, which emerges as a result of the coexistence of an attractive and a repulsive regime in the same tip -monster-interaction.
Conclusions
66 does not significantly affect image quality as long as sharp transitions between attractive and repulsive image regimes are avoided. Thus, the practical considerations for avoiding image quality degradation due to multistability are the same as those used for selecting high-quality SWNT probes6 and avoiding bistability11,12 except for avoiding highly repulsive regimes that favor the occurrence of rupture . Acknowledgments: Santiago Solares and William Goddard were supported by the Microelectronics Advanced Research Corporation (MARCO) and its Focus Center on Functional Engineered Nanoarchitecture (FENA).
SWNT probe TEM image
67 sophisticated type-instance interaction assumptions, which we plan to address in more detail in a future publication. TEM images of the SWNT probe used for the experimental measurements mounted on a conventional silicon tip.
Experimental procedure to image directly above the sample SWNT
Tip sample force curve of SWNT probe with silicon surface
Tip position, nm
Phase space representations
In both cases, there are two distinct solutions for the amplitude, one corresponding to the attractive regime (phase > 90º) and one corresponding to the repulsive regime (phase < . 90º).
Adhesion and friction force parameters and functional forms
- Si(111)-CH 3 step edges
Different values were used depending on the magnitude of the free swing amplitude and whether or not the probe was able to snap during the swing. In all cases, the magnitude of the adhesive force has a maximum at a tip position slightly lower than the initial tip-sample contact point and decreases in both directions, as illustrated in Figure S-5 (a). 74 Table S-1: Magnitude of contact quality factor and maximum adhesion force for simulation results of Figure 6.*.
Remember that the adhesion force only works during the upward movement of the probe after it has contacted the sample. The labels on the curves in Figure S-6 correspond to the MD snapshots in Figure S-7 and show the behavior of the probe as it approaches the sample. Both the amplitude and phase curves show multistability, similar to the curves in Fig. 4 of the paper.
The amplitude curve shows well-defined regions corresponding to the type of oscillation that occurred (Figure S-11): region A is the free oscillation amplitude, regions B and E correspond to the range of cantilever positions for which the probe did not detach. Au nanoparticle, region C corresponds to the range of cantilever positions for which the probe detached the Au nanoparticle each swing but did not reach the surface, and region D corresponds to the range of cantilever positions for which the probe detached from the Au nanoparticle and reached the surface during each swing.
Additional MD parameters
Influence of Carbon Nanotube Probe Tilt Angle on Effective Probe Stiffness and Image Quality in Tapping-Mode Atomic
- Methods
- SWNT and MWNT probe stiffness
- Image distortion for highly tilted probes
- Cantilever oscillation dynamics
- SWNT and MWNT probe stiffness
- Cantilever oscillation dynamics
- Shortcomings of highly tilted probes
- Imaging of sensitive samples
- Challenges and alternatives
- Comparison of force curves between single-walled carbon nanotube and Si tips of comparable radius
- Force curves for single-, double- and triple-walled carbon nanotube probes
- Cantilever oscillation dynamics for A o = 20 nm
- Analysis of tip deformation modes
The tip-sample interaction forces are then integrated into the equation of motion of the oscillating cantilever to simulate AFM action and image construction. Note that in this article “probe stiffness” refers to the effective stiffness of the probe in the vertical direction. In the Supporting Information we provide a comparison between the force curves of a 30.30 SWNT tip and a Si tip with the same radius (~1.7 nm), showing that the tip sample repulsive forces are comparable in both cases are.
Snapshots of the 40,40 SWNT probe shown in Figure 1 approaching a clean Si(100)-OH surface for different values of zts. 103 First, as φ increases, the probe stiffness (as defined in Section 1.0) decreases linearly (Figures 3 and 5), making the probe less sensitive to the fine details of the sample. Third, as φ increases, the probability that tip and sample geometries are incompatible increases.
Comparison of the tip-sample force curves obtained with a 30.30 single-walled carbon nanotube tip and a Si tip (both with radius 1.7 nm) and a 15-nm-radius Si tip.
Density Functional Theory Study of the Geometry, Energetics, and Reconstruction Process of Si(111) Surfaces *
- Overview of the 7x7 DAS structure
- Methods
- Quantum mechanics
- Slab models
- Si(111) surface reconstructions – density functional calculations 1 Energetics
- Geometry Analysis of the DAS 7x7 Reconstruction
- Energy partitioning
- Application of the AECM to real-time reconstruction observations
- Conclusions and prospects
- Pseudopotentials and basis sets
- Slab model calculations
- Comparison of PBE and LDA surface energies
- Comparison of PBE DFT Si(111) surface energies to published values from empirical and semi-empirical calculations
- Comparison of 2x2 hexagonal and rectangular surfaces
Top view of a 7x7 DAS unit cell (a) showing the top five layers (b) after removing the first layer, (c) after removing the first two layers, and (d) after removing the first three layers. Of the 42 atoms in the second layer (red and brown), 36 (red) are bonded to the top adatoms, and 6 (brown) are bonded only to atoms in the third layer (green), leaving a dangling bond. For a 1x1 unit cell, we used 8 k-points in the direction of each of the unit cell vectors.
Using this value, we can analyze the contribution of the dangling bonds to the surface energy of the DAS 7x7 reconstruction. Surface energy for the DAS 5x5 surface model as a function of the spin polarization (number of electrons with unpaired spins). 7-membered rings are not included in the calculation of the surface energy (these rings are present in the c2x8 reconstruction, but the regression analysis performed in the construction of the AECM shows that it is not necessary to assigning energy contribution to them).
The black dots correspond to the average surface energy of the SSC even-sized and irregular-odd-sized structures in the reconstructed region. Calculated surface energy of the DAS 3x3 surface as a function of the spin polarization with respect to the singlet state (Table S-7). 171 Table S-8: Calculated surface energy for the DAS 5x5 surface as a function of the spin polarization with respect to the singlet state.
Structure of the Methylated Silicon (111) Surface Prepared through Hydrogenation-Chlorination-Alkylation *
- Computational Methods
- Periodic DFT Geometry Optimization of 1x1 Unit Cells
- Periodic DFT calculation of Strain Energy at the Step Edges
- Molecular Dynamics Calculations .1 Role of Methyl-Methyl Interactions
184 Since a single stacking fault between the 1st and 2nd Si layers would cause a rotation of the CH3 apparent torsion by 60° relative to the bulk, we performed DFT calculations with stacking faults on Si(111)-H, Si(111)-Cl and Si (111)-CH3. This process is highly exothermic (DFT leads to ΔG kcal/mol after including solvation using the Poisson-Boltzmann continuum model), so the local temperature can increase the mobility of atoms on the surface. 191 All surface unit cell dimensions were based on the calculated equilibrium PBE value of the Si crystal lattice, which is equal to 5.431 Å.
The Si(111)-CH3 1x1 unit cell was modeled using a 2D slab with eight bulk silicon layers, terminated by hydrogen on the bottom surface (Si-H bond perpendicular to the surface). We also calculated the bulk stacking fault energy using a 12-layer 3D periodic bulk model of the silicon crystal. The structure of the Si(111)-CH3 did not change when the cell depth was increased to 4 unit cells deep.
Side view of Si(111)-H periodic unit cells used to calculate the strain energy difference between the <112> (a) and <112> (b) step edge terminations.
