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Chapter 2 Results 2.1 Quantum effects in nanomechanics How will the quantum-size effect in the electron gas in a metallic nanowire affect its mechanical and electrical properties? By modeling a free electron gas confined in the volume of a nanowire Blom et al. [8] showed that stretching a nanowire has an effect on tensile force. It was found to oscillate with the elongation as electron states were pushed over the Fermi level of the metal as the cross section decreases at elongation. One of our objectives was to increase our understanding of a nanosized system like this. How will, for example, the quantum-size affect the transverse force in a metallic nanowire cantilever when it is bent? If it does affect it, how will the oscillating wires resonance frequency be affected? To investigate this we made a model like the one in Blom et al. but bending the wire instead of stretching. We find that there is an effect, which is presented in this section. When a metallic nanowire is bent, its cross section increases which lowers the minimum energy. This can sometimes allow the addition of a new electron to the wire, which will increase the energy in the electron gas due to more electrons in wire. This makes it difficult to bend the wire further. However, bending it even further without any new added electrons will decrease the energy of each electron making the spring softer until it is so bent that a new electron is added and the spring becomes harder again and so on. We obtain a bending dependent spring ”constant”, which make the wires resonance frequency dependent on the amplitude of oscillation. We are starting from the grand canonical potential given by [10, 8] for the T = 0 case Ω = − L 4 2m (EF −En (x))3/2 dx, (2.1) n 0 3 π22 where L is the length of the wire. This equation is the starting point of Paper I. We then need an expression for the energy eigenvalues En (x) of the waves that fits the 15PDF Image | Nanomechanics Quantum Size Effects, Contacts, and Triboelectricity
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