Phonovoltaic Cells: Turning Hot Lattice Vibrations into Electricity

A phonovoltaic cell (often shortened to "pV", with a lowercase p to tell it apart from the photovoltaic "PV") is a proposed solid-state device that converts a particular kind of lattice vibration directly into electrical power. It borrows the architecture of a solar cell, a semiconductor p-n junction, but instead of absorbing particles of light (photons) it absorbs high-energy quanta of vibration (optical phonons). If the phonon carries more energy than the semiconductor's band gap, it can lift an electron from the valence band into the conduction band, creating an electron-hole pair. The built-in electric field of the junction pulls the pair apart, and the separated charges flow through an external circuit as current.

The idea is young. It was set out in a series of papers by Corey Melnick and Massoud Kaviany of the Department of Mechanical Engineering at the University of Michigan, beginning with "Phonovoltaic. I. Harvesting hot optical phonons in a nanoscale p-n junction," published in Physical Review B on 4 March 2016. As of Kaviany's 2021 review in the ASME Journal of Heat Transfer, the phonovoltaic remained a theoretical device. The review states plainly that it "must be demonstrated experimentally." Everything in this article about performance is therefore a prediction from theory and simulation, not a measured result. That caveat matters, and it comes up again in the sections on limits and misconceptions.

Why bother with such an exotic concept? Because the dominant way of turning heat into electricity in solid state, the thermoelectric generator, is inefficient. Phonovoltaics are an attempt to step around the reasons thermoelectrics are inefficient by intercepting energy before it becomes ordinary, disordered heat. To see why that might work, it helps to start with what phonons are and why their "temperature" can differ from the temperature of everything around them.

Phonons in plain English

A crystal is a regular array of atoms held together by chemical bonds that act something like springs. The atoms are never perfectly still. They jiggle about their positions, and because they are coupled to their neighbours, those jiggles travel through the crystal as waves. Quantum mechanics says the energy in each of these vibrational waves comes in discrete packets. Each packet is called a phonon, by analogy with the photon as the packet of light.

Phonons come in two broad families.

• Acoustic phonons are vibrations in which neighbouring atoms move roughly together, in the same direction. At long wavelengths they are literally sound waves. They carry most of the heat in insulating solids and generally have low energies.
• Optical phonons exist in crystals with more than one atom in the basic repeating unit (the unit cell). In an optical mode, neighbouring atoms move against each other. These modes got their name because in ionic crystals they interact strongly with light. They usually have higher and more nearly constant energy than acoustic phonons.

For a phonovoltaic cell, the important point is that optical phonons can carry a well-defined, relatively large packet of energy. In graphite and graphene the most energetic optical phonons carry about 198 to 200 millielectronvolts (meV), according to Melnick and Kaviany's first paper (198 meV) and Kaviany's 2021 review ("200 meV optical-phonon modes"). That is large by the standards of lattice vibrations. Kaviany's review notes that the most energetic optical phonon mode in a typical semiconductor is below 80 meV, and that diamond and cubic boron nitride have optical-phonon cutoff energies around 160 meV.

Energy units and temperature

Physicists often compare energies with the "thermal energy" k_B T, where k_B is the Boltzmann constant (about 8.617 × 10⁻⁵ electronvolts per kelvin) and T is absolute temperature. At room temperature, roughly 300 K, k_B T is about 25.9 meV. Kaviany's review uses the benchmark 5 k_B T ≈ 130 meV at room temperature, and argues that only a limited number of materials have optical phonons above that level, because only light first-row elements form bonds stiff enough to vibrate that energetically.

A graphene optical phonon at 198 meV is therefore about 7.7 times the room-temperature thermal energy. That ratio is why graphene keeps appearing in the phonovoltaic literature.

The core idea: harvesting a narrow band of energy

The Wikipedia article on the topic makes the central point compactly: a phonovoltaic cell "converts only a narrow band of phonon energy," namely the most energetic optical modes. Heat, by contrast, is spread across a broad spectrum of vibrations at many energies. A narrow band of energy has much lower entropy than the same amount of energy spread out as heat, and lower entropy means more of it can, in principle, be turned into useful work.

Kaviany's 2021 review frames the same idea in terms of "phonoelectricity." Thermoelectric harvesters, he writes, have "transformed broad-spectrum, high-entropy heat into a narrow spectrum of low-entropy emissions." Phonoelectricity "in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes a high-entropy heat."

The sequence of events in many real devices goes like this. Something injects energy into electrons: an electric field accelerating them in a transistor, a laser, or a chemical reaction at a surface. Hot electrons shed their excess energy quickly by emitting optical phonons. Those optical phonons then decay, more slowly, by splitting into several lower-energy acoustic phonons, which is the point at which the energy has become ordinary heat. A phonovoltaic cell tries to catch the energy during the middle step, while it is still concentrated in a small number of high-energy optical phonons.

How fast the window closes

The middle step is brief. Measurements on graphite and graphene give a sense of the timescales. Kampfrath and colleagues, writing in Physical Review Letters in 2005, reported that in graphite more than 90 percent of the initially deposited excitation energy goes into a few strongly coupled lattice vibrations within 500 femtoseconds, and they estimated a lifetime of about 7 picoseconds for those hot phonon modes. Later pump-probe measurements on few-layer and multilayer graphene by Wang and colleagues found average hot-phonon lifetimes of about 2.5 picoseconds. A picosecond is a millionth of a millionth of a second.

These numbers explain one of the defining features of a phonovoltaic cell: it has to be tiny. In a few picoseconds, nothing travels far. The device must convert the phonon's energy to an electron-hole pair close to where the phonon was born, before the phonon decays into heat.

How a phonovoltaic cell would work, step by step

The 2016 paper describes the device in terms that track a solar cell closely. Here is the sequence, in plain terms.

1. Excitation. A source creates a population of hot optical phonons inside the junction region. In the papers, possible sources include electrons accelerated by an electric field (as in a transistor channel), laser excitation, and chemisorption of a hot molecular gas. The Wikipedia article lists the same three routes.
2. Generation. A hot optical phonon interacts with a valence electron. If the phonon energy E_p,O is larger than the band gap ΔE_e,g, the phonon can be absorbed and the electron promoted across the gap. The result is an electron in the conduction band and a hole in the valence band.
3. Competition. At the same time, the hot phonon can instead decay into lower-energy acoustic phonons ("downconversion"). Every phonon that downconverts is lost to heat.
4. Separation. The internal electric field of the p-n junction drives electrons toward the n side and holes toward the p side.
5. Collection. Metal contacts on either side collect the carriers. Because they are kept cold (at temperature T_c), the device is a heat engine running between the hot phonon population and the cold contacts.
6. Voltage build-up. As carriers accumulate, the quasi-Fermi levels separate, producing a voltage. Kaviany's review describes how, when the voltage grows large enough, generation is balanced by recombination, just as in a solar cell at open circuit.

Comparison table: thermoelectric, phonovoltaic and photovoltaic

Melnick and Kaviany's first paper includes a comparison of the three device types. The table below is a plain-language adaptation of that comparison.

The table shows why the inventors describe the device as closer to a solar cell than to a thermoelectric. Both the pV and PV cells harvest a nonequilibrium population that is resonant with, or more energetic than, the band gap. A thermoelectric harvests a flow of heat.

Thermodynamic rules the device must obey

The Wikipedia article organises the physics around two classic constraints.

First law: the energy must clear the gap

Energy conservation means the exciting particle must carry at least as much energy as the band gap it is asked to bridge. For a phonovoltaic, that means E_p,O ≥ ΔE_e,g. Since optical phonons carry far less energy than the photons a solar cell absorbs, phonovoltaic materials need very narrow band gaps, on the order of a tenth of an electronvolt to two tenths. The Wikipedia article puts it as a requirement for materials with optical phonon energy of at least 100 meV and a band gap smaller than that.

There is a second, practical requirement that pulls in the opposite direction. The band gap must be much larger than the thermal energy k_B T of the cold contacts. If the gap is too close to k_B T, thermal excitation alone creates many carriers, and the diode "will not function well," in the words of Kaviany's review: the fill factor falls and generation is slowed by the thermally excited electrons. Combining both conditions gives the target summarised in the 2016 abstract: E_p,O ≥ ΔE_e,g ≫ k_B T, plus strong coupling between the phonons and the electrons across the gap.

Second law: the source must be "hotter" than the cell

A heat engine produces work only when it runs between a hot reservoir and a cold one. A solar cell works because the sun's surface, at roughly 6,000 K, is far hotter than a cell at about 300 K, as the Wikipedia article notes. For a phonovoltaic, the "hot reservoir" is the optical phonon population, and its temperature is defined through Bose-Einstein statistics: the number of phonons in a mode is related to the mode energy and a temperature by

n = 1 / (exp(E / k_B T) − 1).

If an external source pumps extra phonons into an optical mode, the occupation n rises above its room-temperature value, and one can define an effective temperature T_p,O for that mode that is higher than the temperature of the acoustic phonons and electrons around it.

Worked example: what does a "hot" optical phonon population mean?

The following is a hypothetical calculation using the Bose-Einstein formula above, for a 198 meV optical mode.

• At 300 K, k_B T ≈ 25.85 meV. E / k_B T ≈ 198 / 25.85 ≈ 7.66. exp(7.66) ≈ 2,120. So n ≈ 1 / 2,119 ≈ 0.00047. On average, fewer than one in two thousand of these modes holds a phonon.
• At an effective 600 K, k_B T ≈ 51.7 meV. E / k_B T ≈ 3.83. exp(3.83) ≈ 46.0. So n ≈ 1 / 45.0 ≈ 0.022.

Doubling the effective temperature of this mode raises its occupation roughly 47-fold. That is the point of the device: even modest-sounding effective temperatures correspond to a dramatic surplus of energetic phonons compared with equilibrium, and that surplus is what the junction tries to harvest.

Why the device must be nanoscale

The single most distinctive requirement of a phonovoltaic is size. Melnick and Kaviany define an electron-phonon cooling length, the distance over which the hot optical phonons and the electrons come into equilibrium. They note that the cooling length is on the order of 100 nanometres in a typical semiconductor. If the distance L between where phonons are excited and where carriers are collected is much smaller than the cooling length, the local nonequilibrium between hot phonons and cold electrons survives, and the device behaves as a phonovoltaic. If L is much larger, the nonequilibrium disappears locally and is replaced by a temperature difference across the device.

The papers describe what happens in the large-device limit. The cell heats up toward equilibrium, the generated electrons relax and carry away only the Peltier heat rather than the full phonon energy, and the device becomes a "thermovoltaic" cell, whose efficiency approaches that of an ordinary thermoelectric. Kaviany's 2021 review states that "a macroscale phonovoltaic generates thermoelectricity," and the Wikipedia article makes the same point: in a macroscale device, the cell behaves as a thermovoltaic (thermoelectric-like) device rather than a phonovoltaic one.

The 2016 paper uses L/(cooling length) = 1 as a rough boundary between the phonovoltaic regime and the thermoelectric regime. In its Monte Carlo simulations, the authors compare 40-nanometre and 400-nanometre cells and find that transport is partly ballistic in the shorter one and diffusive in the longer one. Their standard hydrodynamic model uses a junction "approximately 10 nm" wide as the active region where the phonons are excited.

The thermovoltaic: a family history

The phonovoltaic has an older cousin. Kaviany's review traces its history to the thermovoltaic cell proposed by Span and colleagues (Physica Status Solidi RRL, 2007), in which the hot-side p-metal-n junction of a thermoelectric is replaced by a p-n junction and electron generation events supply the current. Span's group proposed that this could slightly exceed the thermoelectric efficiency limit, but subsequent investigation, according to Melnick and Kaviany, "indicated the TV cell achieves, at most, the TE efficiency." The review adds that "the notion to employ a nanoscale device to exploit the local nonequilibrium between the optical phonons and electrons did not arrive until 2016."

Efficiency: the formulas and what they mean

The 2016 paper and the Wikipedia article both break the predicted efficiency into a product of a few factors. Each factor corresponds to a separate way energy can be lost.

1. The Carnot factor

η_C = 1 − T_c / T_p,O

This is the classical limit for any heat engine running between the hot phonon temperature and the cold contact temperature. It captures how far from equilibrium the phonon population is. The Wikipedia article writes the same expression with the cell temperature T_pV in place of T_c.

2. The fraction of phonons that make electrons

ψ_e-p = γ̇_e-p / (γ̇_e-p + γ̇_p-p)

Here γ̇_e-p is the rate at which hot optical phonons generate electron-hole pairs, and γ̇_p-p is the rate at which they downconvert into acoustic phonons. The ratio is the share of hot phonons that "choose" electricity rather than heat. The papers call this a quantum-efficiency-like quantity. A value near 1 means almost every hot phonon makes a carrier pair; a value near 0 means almost all become heat.

3. The fraction of phonon energy kept by the gap

ΔE_e,g / E_p,O

When a phonon with energy E_p,O creates a pair across a gap ΔE_e,g, any excess energy beyond the gap is quickly lost as the carriers relax to the band edges. So the best a cell can keep is the ratio of gap to phonon energy. This is the same loss that limits single-junction solar cells, where photons with more energy than the gap waste their excess.

4. The figure of merit

Combining the second and third factors gives the phonovoltaic figure of merit:

Z_pV = ψ_e-p × (ΔE_e,g / E_p,O)

Z_pV is at most 1. It is purely a material property: it depends on how strongly the material's electrons couple to its optical phonons, how fast those phonons decay anharmonically, and how closely the band gap matches the phonon energy.

5. The diode factor

A real p-n junction cannot deliver the full band-gap voltage, because of thermal effects at the contacts. The 2016 paper's analytic result (its equation 40) includes a correction:

η_pV ≈ η_C × Z_pV × [1 − 0.75 exp(−η_C ΔE_e,g / (10 k_B T_c))]

The Wikipedia article presents a closely related form with the term written as exp(−0.1 ΔE_e,g / k_B T_pV). Either way, the bracket approaches 1 when the band gap is many times the thermal energy, and it shrinks toward 0.25 as the gap gets small compared with k_B T. The 2016 paper says that when the Carnot factor vanishes the efficiency approaches 0.25 η_C Z_pV, and when T_c vanishes the cell achieves η_pV ≈ η_C Z_pV.

What the formulas say, summarised

Comparing with a thermoelectric

For comparison, the efficiency of a thermoelectric generator is usually written using the dimensionless figure of merit ZT, where Z = S²σ/κ combines the Seebeck coefficient S, electrical conductivity σ and thermal conductivity κ. The standard formula, also given in the 2016 paper, is

η_TE = η_C × (√(1 + ZT) − 1) / (√(1 + ZT) + T_c / T_h).

Melnick and Kaviany note that values of ZT above 1, and thermoelectric efficiencies above 0.2 η_C, "remain challenging to significantly surpass in paired p- and n-type TE legs," because in a thermoelectric the electrons and phonons are in local equilibrium and the Wiedemann-Franz law ties electrical and thermal transport together.

For a sense of where real thermoelectrics stand, NASA's Multi-Mission Radioisotope Thermoelectric Generator (MMRTG), used on Mars rovers, lists a beginning-of-life system efficiency of 6 percent and 110 watts of power, from lead telluride (PbTe) and TAGS thermoelectric materials operating between hot and cold junction temperatures of roughly 540 °C and 210 °C. An Idaho National Laboratory presentation gives the MMRTG's beginning-of-life efficiency as 5.5 percent against a 7.5 percent goal for a proposed enhanced version. These are complete systems and include losses beyond the thermoelectric material itself, but they show why researchers are hunting for alternatives.

Worked example: a hypothetical phonovoltaic against a thermoelectric

The numbers below are illustrative, chosen to show how the formulas interact. They are not measurements of any real device.

Assume the cold contacts sit at T_c = 300 K and the hot optical phonons have an effective temperature T_p,O = 600 K.

• Carnot factor: η_C = 1 − 300/600 = 0.50.
• Take an optical phonon energy of 198 meV (graphene's value) and a tuned band gap of 150 meV. Gap ratio = 150/198 ≈ 0.758.
• Assume 80 percent of hot phonons generate pairs: ψ_e-p = 0.80. Then Z_pV = 0.80 × 0.758 ≈ 0.606.
• Diode bracket: η_C ΔE/(10 k_B T_c) = 0.50 × 150 / (10 × 25.85) ≈ 0.290. exp(−0.290) ≈ 0.748. Bracket = 1 − 0.75 × 0.748 ≈ 0.439.
• Phonovoltaic efficiency: η_pV ≈ 0.50 × 0.606 × 0.439 ≈ 0.133, or about 13 percent.

Now a thermoelectric between 600 K and 300 K with ZT = 1:

• √(1 + 1) ≈ 1.414. Numerator: 1.414 − 1 = 0.414. Denominator: 1.414 + 300/600 = 1.914.
• η_TE = 0.50 × 0.414 / 1.914 ≈ 0.108, or about 11 percent.

In this hypothetical case, the phonovoltaic edges out the thermoelectric. If the figure of merit is raised to 0.9 with the same other assumptions, the phonovoltaic estimate rises to about 0.50 × 0.9 × 0.439 ≈ 0.198, roughly 20 percent. That pattern matches the authors' broader conclusion: their paper states that, unless the figure of merit exceeds about 0.7, significant nonequilibrium is required to outperform a thermoelectric with ZT = 1.

Two important caveats apply. First, a real device would have to achieve that 600 K effective phonon temperature in a nanoscale junction while keeping the contacts at 300 K, which is the hard part. Second, a thermoelectric harvests heat that already exists, while a phonovoltaic must be paired with a source that creates hot optical phonons. They are not drop-in substitutes for each other.

The authors' headline predictions

The 2016 paper's hydrodynamic simulations conclude that "with a resonant and energetic optical phonon mode which primarily generates electrons, the pV cell triples the efficiency of a TE with ZT = 1," and that "even under reduced nonequilibrium, such a pV cell doubles the TE efficiency." The authors immediately add that "finding and tuning a material with these properties is challenging."

The Wikipedia article adds that if the band gap and optical phonon are resonant and the phonon favours electron generation, efficiency can approach the Carnot limit as the cell temperature approaches absolute zero. That is a theoretical limit, not a practical operating point.

The microscopic physics: two competing couplings

Whether a material works as a phonovoltaic comes down to a race between two processes. The papers calculate both from first principles.

Electron-phonon coupling

When an optical phonon displaces the atoms, it changes the electric potential that electrons feel. If that change is large enough to mix the highest occupied electronic state with the lowest unoccupied one, the phonon can be absorbed and an electron promoted across the gap. The 2016 paper describes this with an illustration in which a phonon displaces atoms and perturbs the highest occupied state so that it overlaps with the lowest unoccupied state.

The rate is calculated using Fermi's golden rule, with a matrix element obtained by expanding the electron potential in the atomic displacements. The Wikipedia article and the papers cite the density-functional perturbation theory framework reviewed by Baroni and colleagues in Reviews of Modern Physics (2001) as the computational basis.

Phonon-phonon coupling (downconversion)

Real crystal bonds are not perfect springs. Their anharmonicity lets one high-energy phonon split into two or more lower-energy phonons. The papers model this using third-order force constants, citing the method of Hellman and Abrikosov (Physical Review B, 2013) for temperature-dependent effective force constants from first principles. This downconversion channel is the main enemy of a phonovoltaic: each phonon that downconverts produces heat and entropy instead of a carrier pair.

Why strong bonds usually mean big gaps

A deep difficulty, set out in Kaviany's review, is that the material properties a phonovoltaic needs tend to work against each other. Energetic optical phonons need light atoms joined by stiff bonds. But strong bonds "also localize electrons while opening a large bandgap." In most materials, therefore, either the band gap is far larger than the optical phonon energy, or the optical phonon energy is barely above k_B T.

The review gives an illustration from the other extreme. Soft materials with a metal-semimetal-semiconductor transition, such as mercury cadmium telluride (HgCdTe), can have band gaps comparable to their phonon energies, but these materials "hold extremely weak bonds" and have optical phonons below 25 meV. That is too close to room-temperature thermal energy to work.

Graphene: the leading candidate

Graphene is the exception that drives the field. Kaviany's review explains why. Its sp² hybridised carbon-carbon bonds produce extremely energetic optical phonon modes (around 200 meV), while the hybridisation and crystal symmetry allow the fourth, π-bonded electron on each carbon to move freely, giving a semimetal with no band gap at all. Pristine graphene thus has the energetic phonons but lacks the gap. The research question becomes: can a gap be opened and tuned to sit just below the optical phonon energy without destroying the strong electron-phonon coupling?

The papers and the Wikipedia article list several ways to open a gap in graphene, each drawn from earlier literature:

• Uniaxial strain (Pereira and colleagues, Physical Review B, 2009, using a tight-binding approach).
• An electric field across bilayer graphene (Park and colleagues, Physical Review Letters, 2015).
• Chemical doping or functionalisation (reviewed by Georgakilas and colleagues in Chemical Reviews, 2012).

Paper II: hydrogenated graphite

In "Phonovoltaic. II. Tuning band gap to optical phonon in graphite" (Physical Review B 93, 125203, 2016), Melnick and Kaviany used density functional theory to tune graphite's band gap by partial hydrogenation and by isotropic strain. They identified a stable partly hydrogenated structure with the gap and optical phonon energy matched near 200 meV. But hydrogenation shifted the relevant electronic bands from π-type to σ-type, which suppressed the electron-phonon coupling. Most optical phonons then downconverted, and the figure of merit stayed below 0.1. The first paper's abstract summarises the result: "hydrogenation degrades the strong electron-phonon coupling in graphene such that the figure of merit vanishes." The value of Paper II was methodological: it set out how to tune and evaluate a candidate material.

Paper III: graphene doped with boron nitride

In "Phonovoltaic. III. Electron-phonon coupling and figure of merit of graphene:BN" (Physical Review B 94, 245412, 2016), the authors turned to graphene in which some carbon atoms are replaced by boron and nitrogen. Hexagonal boron nitride has the same honeycomb structure as graphene, so mixing the two can open a gap while preserving much of graphene's character.

Accounts of the predicted figure of merit differ slightly between sources. The Wikipedia article reports a predicted Z_pV of 0.65 for graphene:BN and says the authors estimated this could give twice the efficiency of a typical thermoelectric generator. Kaviany's 2021 review states that in graphene:BN the electron-phonon coupling "does not depend on the BN concentration" but is weakened slightly, limiting ψ_e-p below 0.75 and therefore the figure of merit below 0.6, which "still enables phonoelectricity generation with an efficiency of up to 0.5 η_C." Both sources agree that graphene:BN retains a substantial figure of merit, unlike hydrogenated graphene.

The review also describes two ways of arranging the boron and nitrogen: an ordered scheme, in which boron atoms replace carbon on one sublattice and nitrogen on the other, and a disordered scheme, in which both are spread across both sublattices.

Bilayer graphene and the phonovoltaic transistor

A 2017 paper, "Bilayer graphene phonovoltaic-FET: In situ phonon recycling" (Physical Review B 96, 205444), took the idea in a practical direction. Its abstract reports that ab initio calculations give bilayer graphene under a cross-plane field a figure of merit "exceeding 0.9." At room temperature, a phonovoltaic made from it could recycle 65 percent of a highly nonequilibrium, minimum-entropy phonon population.

The paper then simulated a bilayer graphene field-effect transistor (FET) using full-band Monte Carlo methods. In a transistor, electrons accelerated by the channel's electric field emit hot optical phonons as a matter of course. The simulations found that those phonons could be recycled in situ with only about 50 percent efficiency, and that this efficiency fell as the field strength increased. The authors nevertheless concluded that a well-designed FET-phonovoltaic could recover heat from the transistor far more efficiently than a thermoelectric generator could harvest the same heat from outside the device.

Kaviany's review explains why bilayer graphene does well: its electronic density of states increases near the band edge, so ψ_e-p rises as the gap approaches the phonon energy.

Candidate materials compared

Device design requirements

The 2016 hydrodynamic simulations produced a short list of requirements beyond material choice. In the authors' conclusions:

1. Maximise the active volume. The region where optical phonons are excited should fill most of the device, unless hot phonon relaxation is slow compared with phonon transport.
2. Block minority carriers from the contacts. Surface recombination at the contacts must be hindered. When minority carriers can reach a contact and recombine, a large adverse current develops. The paper treats suppressed surface recombination as "a requirement for efficient operation."
3. Make the junction strong enough. The difference in Fermi energy across the p-n junction should exceed η_C ΔE_e,g, without slowing generation.

The paper also found that a large ψ_e-p increases efficiency significantly beyond the linear relationship predicted by the simpler analytic model.

Applications people have proposed

Because no phonovoltaic has yet been built and tested, "applications" here means the uses that researchers have argued would make sense if the device works.

Recycling heat inside electronics

The clearest proposal is the one in the 2017 bilayer graphene paper: recovering energy from the hot optical phonons that transistors already generate. When electrons are accelerated by a field in a transistor channel, they lose energy by emitting optical phonons, which then decay into heat. A phonovoltaic integrated into the transistor could, in principle, turn part of that energy back into electricity before it heats the chip. The paper's own numbers (around 50 percent recycling efficiency in the simulated FET, falling at higher fields) give a sense of what theory suggests is possible.

Solid-state heat harvesting at small scales

The 2016 paper motivates the phonovoltaic by pointing out that thermoelectric effectiveness "vanishes in nanoscale and microscale devices, where the contact resistance dominates the thermoelectric effects." A device that works best at the nanoscale would fill a gap that thermoelectrics leave.

Chemical energy and surfaces

The Wikipedia article mentions chemisorption of a hot molecular gas as a way to create hot optical phonons. In principle, energy released when molecules bond to a surface could be harvested this way. Kaviany's review places phonovoltaics within a broader "atomic-level energy conversion" programme that also includes phonon recycling in laser cooling and phonocatalysis.

Limits and open problems

No experimental demonstration yet

Kaviany's 2021 review describes the phonovoltaic as "the sole example of a phonoelectric device, requiring substantially more study," and states that "most importantly, it must be demonstrated experimentally." Every efficiency figure in this article comes from theory or simulation.

Materials are scarce

The authors repeatedly stress that finding a suitable material "remains very challenging." The requirements, an energetic optical phonon, a gap tuned just below it, a gap well above k_B T, and strong interband electron-phonon coupling, rule out almost everything. The review notes that the likelihood of success "would be greatly increased if nongraphene-based materials were established with a large figure of merit and could be incorporated in 3D devices."

Scale cuts both ways

The nanoscale requirement means a single cell can only intercept phonons in a tiny volume. Making the device larger destroys the local nonequilibrium that it depends on and turns it into a thermoelectric. Any large-scale use would have to rely on many nanoscale junctions, or on integration directly where hot phonons are produced, as in the transistor proposal.

Fabrication challenges

Opening and precisely tuning a band gap in graphene to within a fraction of the phonon energy, building a strong p-n junction in that material, suppressing surface recombination at the contacts, and keeping the contacts cold while the junction region is driven far from equilibrium are each significant engineering tasks. The papers identify these requirements but do not claim to have solved them.

Efficiency depends on the source

The overall efficiency of any system using a phonovoltaic depends on how efficiently hot optical phonons are created in the first place. If a laser or an electric field is used to create them, that step has its own losses. The phonovoltaic efficiency formulas describe only the conversion of an existing hot phonon population into electricity.

Common misconceptions

"A phonovoltaic turns sound into electricity." Not really. Sound waves are low-energy acoustic phonons. A phonovoltaic targets high-energy optical phonons, and its whole design is about catching them before they turn into acoustic phonons. It is not a vibration energy harvester of the kind that uses piezoelectric materials to capture mechanical shaking.

"It is a better thermoelectric." The device shares a goal with thermoelectrics (making electricity from thermal energy), but it works differently. A thermoelectric harvests a heat flow across a temperature difference. A phonovoltaic harvests a nonequilibrium population of specific vibrations inside a tiny junction. Scale it up, and the authors say it becomes a thermoelectric-like thermovoltaic.

"It can beat the Carnot limit." No. Every formula in the literature includes the Carnot factor η_C as a ceiling. The claim is that a phonovoltaic might get closer to Carnot than a thermoelectric does, because it harvests a low-entropy, narrow band of energy.

"Graphene phonovoltaics already exist." As of the 2021 review, the device had not been demonstrated experimentally. Graphene is a predicted candidate based on ab initio calculations.

"Phonovoltaics will replace solar panels." They harvest a completely different energy source. A solar cell absorbs photons arriving from outside. A phonovoltaic absorbs phonons created inside a material. They are analogues, not competitors.

The bigger picture: where phonovoltaics sit in energy conversion

It helps to place the phonovoltaic within the family of direct energy converters, devices that skip the step of turning energy into heat and then into mechanical motion.

• Photovoltaics convert photons to electricity. The theoretical ceiling for a single-junction solar cell under standard sunlight, the Shockley-Queisser limit, is about 33.7 percent at a band gap of 1.34 eV, according to the Wikipedia article on the limit. The original 1961 calculation by William Shockley and Hans-Joachim Queisser gave about 30 percent at 1.1 eV. The same physics, excess energy above the gap being wasted, appears in the phonovoltaic gap-ratio factor.
• Thermoelectrics convert heat flow to electricity through the Seebeck effect, with practical system efficiencies in the single digits, as the MMRTG example shows.
• Thermovoltaics replace one thermoelectric junction with a p-n junction but, according to Melnick and Kaviany, achieve at most thermoelectric efficiency.
• Phonovoltaics convert nonequilibrium optical phonons to electricity, and are predicted (not yet shown) to exceed thermoelectrics under the right conditions.

Kaviany's review frames this as a contrast between two strategies for handling heat. One strategy waits until energy has become broad-spectrum heat and then tries to concentrate it. The other, phonoelectricity, intervenes earlier, while energy is still in a low-entropy form. The phonovoltaic is the first worked-out device design built on the second strategy.

Timeline

The first paper acknowledges support from the National Science Foundation program on Thermal Transport and Processes (award CBET-1332807) and computing resources at the US Department of Energy's National Energy Research Scientific Computing Center.

Frequently asked questions

What does "phonovoltaic" mean? It combines "phonon" (a quantum of lattice vibration) with "voltaic" (producing a voltage), by direct analogy with "photovoltaic."

Who proposed it? Corey Melnick and Massoud Kaviany of the University of Michigan, in a series of Physical Review B papers beginning in 2016.

Has anyone built one? Not according to the most recent review from the originating group (2021), which says the device must still be demonstrated experimentally.

What is the most promising material? Graphene-based materials. Theory predicts that bilayer graphene under a cross-plane electric field could reach a figure of merit above 0.9, and that graphene doped with boron nitride could reach roughly 0.6 to 0.65. Hydrogenated graphene was predicted to fail.

Why must it be so small? Because the hot optical phonons and the electrons come to equilibrium over a cooling length of around 100 nanometres in a typical semiconductor. The device has to convert phonon energy within that distance, or it behaves like an ordinary thermoelectric.

How efficient could it be? The authors' simulations suggest that a cell made from an ideal material could double or triple the efficiency of a thermoelectric with ZT = 1. That is a theoretical prediction under specific assumptions, including a strongly nonequilibrium phonon population in a nanoscale junction.

What is the figure of merit Z_pV? The product of two fractions: the share of hot optical phonons that generate electron-hole pairs rather than decaying into heat, and the share of the phonon's energy that the band gap preserves. It runs from 0 to 1.

Where would the hot phonons come from? From electrons accelerated by an electric field (as in a transistor), from laser excitation, or from chemical processes such as a hot gas bonding to a surface.

Is this the same as a piezoelectric energy harvester? No. Piezoelectric harvesters convert mechanical strain, such as vibrations from machinery or footsteps, into charge. A phonovoltaic converts specific high-energy atomic vibrations into electron-hole pairs in a semiconductor junction.

Could it make computer chips more efficient? That is one of the main proposals. Simulations of a bilayer graphene transistor suggest that about half of the energy in hot phonons generated in the channel could be recycled, though this fell at higher fields. Whether this can be realised in practice is unknown.

Summary

The phonovoltaic cell is a theoretical device that applies the logic of a solar cell to lattice vibrations. It aims to catch energy while it is still concentrated in a narrow band of high-energy optical phonons, and to convert it to electricity in a p-n junction before it spreads out into disordered heat. The theory, developed mainly by Melnick and Kaviany between 2016 and 2021, shows that such a device could outperform thermoelectric generators if three things come together: a material with energetic optical phonons and a band gap tuned just below them, strong coupling between those phonons and electrons across the gap, and a nanoscale junction kept far from equilibrium. Graphene-based materials are the leading candidates on paper. The concept's biggest open question is the simplest one: whether it can be made to work in a laboratory.

Sources

• Phonovoltaic (Wikipedia)
• Melnick and Kaviany, "Phonovoltaic. I. Harvesting hot optical phonons in a nanoscale p-n junction," Physical Review B 93, 094302 (2016), author PDF
• Melnick and Kaviany, "Phonovoltaic. II. Tuning band gap to optical phonon in graphite," Physical Review B 93, 125203 (2016), NASA ADS record
• Melnick and Kaviany, "Phonovoltaic. III. Electron-phonon coupling and figure of merit of graphene:BN," Physical Review B 94, 245412 (2016)
• Melnick and Kaviany, "Bilayer graphene phonovoltaic-FET: In situ phonon recycling," Physical Review B 96, 205444 (2017), OSTI record
• Kaviany, "Atomic-Level, Energy-Conversion Heat Transfer," ASME Journal of Heat Transfer 143, 090801 (2021)
• Melnick and Kaviany, "From thermoelectricity to phonoelectricity," Applied Physics Reviews 6, 021305 (2019), bibliographic record
• Kampfrath et al., "Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite," Physical Review Letters 95, 187403 (2005)
• Wang et al., "Ultrafast Relaxation Dynamics of Hot Optical Phonons in Graphene" (arXiv:0909.4912)
• NASA, Multi-Mission Radioisotope Thermoelectric Generator fact sheet
• Shockley-Queisser limit (Wikipedia)