Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2021 / Paper 1 / 7

Three standard approaches are piezoelectric, electromagnetic and electrostatic energy harvesting.

In all three cases the output is constrained by the available mechanical input and damping. Nanoscale dimensions alone do not supply an energy advantage.

A thermocouple uses two materials with different Seebeck coefficients. With their junctions at different temperatures, the net open-circuit voltage isUsing p-type and n-type legs makes the two contributions add. Many pairs can be connected electrically in series to add voltage while remaining thermally in parallel between the same hot and cold plates. A single homogeneous wire does not provide this same complete-circuit voltage when its return lead has the same thermopower.

The reciprocal Peltier effect transports heat when electric current passes through a junction. The Kelvin relation $\Pi =\alpha T$ connects the heat carried per unit charge to the Seebeck coefficient. The same combination of large thermopower, high electrical conductivity and low thermal conductivity gives a favorable dimensionless figure of meritThus materials useful for a generator are also useful for a cooler when electric current is driven in the appropriate direction. Joule heating and thermal leakage oppose cooling; device geometry, contact resistance and operating temperature must still be appropriate. Reversibility of the thermoelectric coupling does not make either device lossless.

A pyroelectric material has a spontaneous electric polarization that changes with temperature. electrodes collect the resulting change in compensating charge. For a uniform element,Consequently temperature variation in time, rather than a steady temperature difference alone, drives a pyroelectric generator. A cyclic thermal input and a suitable electrical circuit are needed for repeated energy extraction.

The primary pyroelectric effect is the change of electric polarization at fixed strain. The secondary pyroelectric effect arises because thermal expansion strains a piezoelectric crystal and thereby changes its electric polarization. In component notation its contribution iswith piezoelectric coefficients $e_{ij}$ and thermal-expansion coefficients ${\alpha }_j$. Choosing orientation, mechanical constraint and substrate expansion so that the secondary contribution reinforces the primary one can increase the response; the signs can instead oppose one another.

An array of slender nanowires can expand more freely than a film clamped to a substrate and can exchange heat rapidly because of its high surface-to-volume ratio. Reduced clamping can recover a secondary response suppressed in the film. Faster thermal cycling can also increase electric current through $dT/dt$. This is a geometrical opportunity rather than a universal increase of the intrinsic coefficient: screening, leakage, orientation and the actual thermal excursion must be compared. ZnO nanowire generators provide an experimental realization of pyroelectric energy conversion.^[ref]

Treat the film as a parallel-plate capacitor, initially compensated and then isolated electrically. Its capacitance and temperature-induced electric polarization charge areThe corresponding ideal open-circuit signal, with the electrode polarity defined consistently with this charge convention, isArea cancels because both charge and capacitance are proportional to it. Substitution givesThe voltage magnitude is approximately $0.99\mathrm{V}$; interchanging the voltmeter leads reverses its sign. This is an ideal capacitive result, before leakage, mobile-charge screening or loading by the measurement circuit reduces the signal.