Nonlinear current-induced forces in Si atomic wires

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 16, 2003, Pages

  Yang, Zhongqin ^a   Di Ventra, Massimiliano ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SILICON;

ARTICLE; CALCULATION; ELECTRIC CURRENT; ELECTRONICS; FORCE; MATHEMATICAL MODEL; NONLINEAR SYSTEM;

EID: 2942598326     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.161311     Document Type: Article

References (31)

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22. Note that this definition of direct force is not unique in literature (see, e.g., Ref. 13). Furthermore, the part of the “electron wind force” defined in the literature (see Ref. 13) as due to the energy transfer from the electrons to the ions is estimated to be very small in the present case. For instance, for a 3-Si wire and a bias of 0.1 V the electric current is about (Formula presented) Assuming a typical mean-free path of 1000 Å for ballistic conduction, we obtain a collision time of (Formula presented) at the gold Fermi velocity. During this collision time there are, on average, about five collisions due to current flow. An upper bound of the force per collision is the change of momentum due to an electron at the right Fermi level that scatters to the left Fermi level. The total force is then the sum of this force over all collisions, i.e., (Formula presented) which is one order of magnitude smaller than the force due to the redistribution of charge (see Fig. 11). This estimate increases with the square root of the bias and is thus one to two orders of magnitude smaller than the force we discuss in the text.
23. We neglect local heating effects that might contribute to mechanical deformations of the wires. See, e.g., Y.-C. Chen, M. Zwolak, and M. Di Ventra, cond-mat/0302425 (unpublished).
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29. Similar considerations explain the almost linear dependence of the force on the single-atom wire [see Fig. 11(d)]. In this case, the extra charge on the atom is almost zero at any bias with consequent constant contribution from the discrete spectrum, and linear contribution from the continuum spectrum as a function of bias.
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31. Using the tight-binding approach, T. N. Todorov, J. Hoekstra, and A. P. Sutton, have shown that in linear response the largest current-induced force is almost constant for wire lengths of three atoms or more (Ref. 7). We show here that this trend is also valid for the average force of Si wires at any bias.