Page 66 - Principles and Applications of NanoMEMS Physics

2. NANOMEMS PHYSICS: Quantum Wave-Particle Phenomena 53

where κ is a scaling factor that models the effects of surface topography,
including for instance, the anchor step-up and its corresponding finite
elasticity, E is the Young’s modulus of the beam material, ρ its density, h
its thickness and L its length, the combined amplitude of AC and DC
r
voltages is chosen to be lower than pull-in, thus keeping the beam from
collapsing.

2.2.2.2 Coulomb Blockade

The phenomenon of Coulomb blockade [68, 69] refers to the fact that
under certain conditions, namely, when junctions are defined whose
− 15
capacitance is of the order of C ~ 10 F or less, the energy required to
increase the charge by one electron is not negligible with respect to
temperature. For example [68], Figure 2.3 shows that, while a neutral
metallic island, such as the plates of a capacitor, emits no electric field and,
thus, allows the unimpeded approach of an electron, once this electron
becomes part of the island it emits an electric field that may prevent the
addition of more electrons.

Figure 2-4. (a) Charging Coulomb island. (a) Charging energy of small capacitor.

At this point, the island blocks such an addition of extra charge. For a
− 15
junction capacitance of C ~ 10 F , the minimum voltage required to add a
charge q is q C , thus the charging energy is
E = q 2 C = . 1 283× 10 − 23 J , which is close to the thermal energy at 1K.
2
C
If the capacitance were smaller, e.g., C ~ 2 . 6 × 10 − 18 F , such as might be