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2.2 Electrically charged nanocontacts 21 Fr (pN) U = 7V 0.2 0.0 - 0.2 - 0.4 - 0.6 - 0.8 5 Repulsive U = 3.5 V 10 15 20 r (nm) van der Waals D = 1.5 nm R = 3.0 nm Attractive Figure 2.4: Radial dipole force on an adatom using D = 1.5 nm and R = 3.0 nm and our values of μ and α for two different voltages U, one above and one below U0 = 3.7 V. The van der Waals force has been calculated and plotted in the figure using D = 1.5 nm. For D < 1.5 nm the van der Waals force becomes important for the radial force on the adatoms. where z is the height over the surface for the center of the adatom, about one adatom radius. We see that the distance z only affects Fz , not Fr . We are now able to calculate the electrostatic forces on the adatom on the surface under the tip. The calculation above is valid for the first step in the mound formation where the surface still may be considered as flat. Setting Fr = 0 in the expression above then yields where U 2/3 r0 = (D + R) U 0 μD(D + R)2 U0 = αR(2D+R). − 1, (2.24) (2.25) Inserting the equation for the threshold voltage U0 into the equation for the electric field E ≈ Ez yields for r = 0 where a mound of radius zero will form the threshold field for mound formation E0 = μ/α ≈ 2 V/nm. What about the van der Waals force? We find that it can be neglected compared to the electric dipole force for tip-to-surface distance D larger than 1.5 nm. In this section we have seen that due to the competition between the surface in- duced dipole moment and the electric field induced dipole moment of the adatom, the sign of the dipole vector depends on the electric field strength for a positive tip.PDF Image | Nanomechanics Quantum Size Effects, Contacts, and Triboelectricity
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