Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 1 / Section B / 12

Specific energy is usable energy divided by device mass, commonly $\mathrm{Wh}\mathrm{k}{\mathrm{g}}^{-1}$; specific power is deliverable power divided by mass, commonly $\mathrm{W}\mathrm{k}{\mathrm{g}}^{-1}$. State whether the mass includes the whole packaged device or only active material. Volumetric energy density uses volume instead.

A conventional capacitor separates charge across a dielectric and stores $U=C{V}^2/2$, enabling rapid charge/discharge but relatively little energy. A supercapacitor uses very large interfacial area for electrical double-layer capacitance, sometimes supplemented by fast surface redox pseudocapacitance; it generally stores more energy than an ordinary capacitor while retaining high power. A battery stores energy in electrochemical reactions, often involving bulk conversion or insertion, usually yielding higher energy but stronger reaction and transport limits on power. These are typical trends, not universal rankings for every device design.

A primary battery is intended for a single discharge; a secondary battery is designed for repeated electrical recharge through sufficiently reversible reactions. A microbattery is defined by its small dimensions or microfabricated construction, not by rechargeability. Therefore microbatteries can belong to either class. A thin-film Li-ion microbattery with reversible insertion electrodes is secondary because lithium can shuttle back and forth during discharge and charging; a miniature cell using irreversible primary chemistry remains primary. Small size alone does not justify assigning every microbattery to the secondary class.

Two electrons are transferred per formula unit of Li2O2. Its theoretical specific capacity isAt $3\mathrm{V}$, the corresponding theoretical specific energy is $3q=3.50\mathrm{Wh}{\mathrm{g}}^{-1}$, or $3500\mathrm{Wh}\mathrm{k}{\mathrm{g}}^{-1}$. The mass basis is Li2O2, equivalently the combined stoichiometric masses of consumed Li and O2; a value normalized to Li metal alone would be different.

A real lithium-air battery also includes electrolyte, porous positive-electrode support, separator, current collectors, excess reactants, packaging and possibly oxygen treatment. Insulating Li2O2 can block pores and electron transport, limiting utilization; polarization, electrolyte decomposition, moisture/CO2 contamination and parasitic reactions lower useful voltage and reversible capacity. A lithium-ion battery instead shuttles Li ions between pre-existing host electrodes, generally in a closed cell without consuming atmospheric oxygen; the oxygen/peroxide reaction and its mass/transport requirements make the Li-air mechanism distinct.

The Shockley-Queisser limit is the detailed-balance efficiency bound for an ideal single-junction solar cell with radiative recombination under specified illumination and optical conditions. Below-gap photons are not absorbed and excess energy of above-gap photons is thermalized; radiative emission further limits the output voltage. The often quoted unconcentrated terrestrial maximum is roughly one third, not an illumination-independent universal percentage.

A multi-junction solar cell places a high-gap junction before lower-gap junctions, dividing the spectrum so photons generate carriers in a better-matched absorber. This reduces transmission and thermalization losses and can exceed the single-junction bound without violating its assumptions: there is now more than one junction. In a two-terminal series stack, all junctions carry the same current, so the lowest photocurrent limits the whole device. Current matching uses bandgap choice, absorber thickness, optical management and sometimes lateral area to make the generated currents comparable for the intended spectrum. Independently contacted junctions need not share the same current.^[ref]

The longest wavelength capable of producing an above-gap electron-hole pair isEvery transmitted wavelength is longer than $600\mathrm{nm}$, so every transmitted photon has energy below $2.4\mathrm{eV}$. Consequently the ideal single-photon absorber generates no photocurrent and $\boxed{\eta =0\%}$. The stated irradiance does not change this spectral-threshold conclusion. Defect-mediated or multiphoton absorption is outside the assumed ideal band-to-band model.