Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2019 / Paper 1 / Section B / 12

A thermoelectric generator uses the Seebeck effect and needs a spatial temperature gradient: a couple develops $V\simeq (S_p-S_n)\Delta T$ between hot and cold junctions. It can deliver continuous power under a steady thermal gradient and has no moving parts, but requires sustained heat flow and adequate hot- and cold-side thermal contacts. Thermal conduction, internal electrical resistance and the material's thermoelectric figure of merit limit conversion.

A pyroelectric generator responds to a time-dependent spontaneous electric polarization. Under approximately uniform heating or cooling, $I=pAdT/dt$ when the electrical boundary condition allows charge flow. It can harvest temporal thermal fluctuations without a persistent spatial gradient. However, at a constant uniform temperature its ordinary pyroelectric current stops; practical extraction needs cycling, low-leakage electronics and a suitable load. A large open-circuit voltage is not evidence of a large available average power. Temperature-driven nanowire measurements provide a primary experimental example of this distinction.^[ref]

For electrode area $A$, the change in spontaneous polarization density supplies a charge scale $\Delta Q=pA\Delta T$, while the film's capacitance is $C=\epsilon A/d$. The voltage magnitude is therefore $|\Delta V|=|p|d|\Delta T|/\epsilon$. More explicitly, for an initially compensated film with no change in free electrode charge, $\Delta D=\epsilon \Delta E+p\Delta T=0$. Taking $z$ from the lower electrode to the upper one gives $\Delta V_{\mathrm{upper}-\mathrm{lower}}=-d\Delta E=pd\Delta T/\epsilon$.The measurable magnitude is $0.339\mathrm{V}$, with polarity reversed by reversing the poling direction or the temperature change. This is an ideal open-circuit estimate: leakage, the measuring instrument's input capacitance and finite charge-relaxation time can reduce or reshape the observed voltage.

The secondary pyroelectric effect is the change of polarization density produced when thermal strain acts through piezoelectricity. It is additional to the primary change at fixed strain. A linear constitutive description along the polar axis iswhere $e_{3j}$ are piezoelectric stress coefficients and ${\alpha }_j$ the freely developing thermal strains per kelvin. Thermal-expansion mismatch with a support or a deliberately chosen compliant structure can change the secondary contribution. It enhances the total response only if its sign reinforces the primary response; mechanical boundary conditions and thermal cycling must be characterized rather than assuming every restraint is beneficial.

Preventing axial expansion removes the free axial-strain contribution, but does not automatically eliminate every secondary contribution. In a one-dimensional idealization with only ${\epsilon }_3$ coupling and perfect axial clamping, that strain-mediated term vanishes. A real rod may still expand transversely, and nonzero $e_{31}$ or $e_{32}$ can change $P_3$ through those strains. In a stress-based constitutive equation, the same restraint appears as thermal stress and a piezoelectric term; do not add it a second time to a coefficient already specified for the constrained condition. Full suppression of all relevant thermal strains leaves the primary coefficient at fixed strain. The answer therefore depends on which degrees of freedom are constrained, not simply on the word “nanorod”.

A wireless sensor node combines a sensor, signal conditioning and conversion, a processor, a radio and a power subsystem. It can use a battery, a wired supply where practical, or local harvesting such as light, vibration or a thermal gradient, usually with a storage capacitor, supercapacitor or rechargeable battery to bridge interruptions. Harvested power must meet the time-averaged demand and storage must supply peak radio current.

Reduce power by duty cycling the sensor, processor and radio; use a low-leakage sleep mode and switch off unused peripherals. Buffer and batch data, transmit fewer unnecessary bits, use event-triggered acquisition when it meets the application, and reduce retries with a reliable link and an appropriate transmit-power level. Include wake-up, sensing, processing and communication energy in the budget: reducing payload alone may not reduce a radio dominated by startup overhead.

The duty cycle $D=t_{\mathrm{active}}/(t_{\mathrm{active}}+t_{\mathrm{sleep}})$ is the fraction of time spent active. At a constant supply voltage and with switching energy neglected,For $D=0.01$, the average current is $0.01(25\mathrm{mA})+0.99(6.1\mu \mathrm{A})=256.039\mu \mathrm{A}$. Thus $\bar{P}=512.078\mu \mathrm{W}\simeq 0.512\mathrm{mW}$. Multiplying only the active power by the duty cycle would omit the sleep contribution.

For $D=0.001$, the same duty cycle model gives $\bar{I}=25\mu \mathrm{A}+0.999(6.1\mu \mathrm{A})=31.0939\mu \mathrm{A}$. Thus $\bar{P}=62.1878\mu \mathrm{W}$. The tenfold reduction in active fraction reduces average power by only about $8.23$ because the sleep current remains. The ideal limit as $D\to 0$ is $V{I}_s=12.2\mu \mathrm{W}$, before leakage elsewhere or wake-up energy. Active and sleep contributions become comparable at a duty cycle of roughly $I_s/(I_a+I_s)=0.0244\%$; below that scale lowering sleep current is particularly valuable.