Green's Third Generation Photovoltaics (2006, ch. 7) posed the problem of realizing carrier multiplication — one absorbed photon creating two or more electron-hole pairs via impact ionization or related mechanisms — as a practical route beyond the single-junction efficiency limit, with ideal limiting efficiencies of 85.9% (concentrated direct light) and 43.6% (diffuse light) but negligible measured gains in bulk semiconductors (silicon internal quantum efficiency below 1.05 at 350 nm). The unresolved core is whether material engineering can suppress the competing relaxation processes — hot-carrier cooling by phonon emission and Auger recombination, the microscopic time-reverse of impact ionization — without introducing losses that negate the gain. Twenty years of literature transformed the materials science (multiple exciton generation in Pb-chalcogenide quantum dots, van der Waals semiconductors, monolayer MoSe2, perovskite nanocrystals, and Bi2Se3, with device-harvested external quantum efficiencies above 100%), but no photovoltaic device has yet demonstrated a net efficiency benefit attributable to carrier multiplication, so the practical-benefit question remains open.

Background

In a conventional single-junction solar cell, each photon with energy above the semiconductor bandgap creates one electron-hole pair; the pair is born 'hot' (with the photon's excess energy) and cools to the band edges within picoseconds by emitting phonons (lattice vibration quanta), so the excess energy is lost as heat. The Shockley-Queisser detailed-balance analysis (comparing radiative emission and absorption of a single junction) caps single-junction sunlight-to-electricity efficiency near 33%. A long-proposed route beyond this cap is impact ionization: a hot carrier collides with a valence-band electron and transfers its excess energy to it, creating a second electron-hole pair, so that the internal quantum efficiency (IQE, collected carriers per absorbed photon) can exceed one. One photon generating several pairs is called carrier multiplication (CM); in quantum-confined nanocrystals it is called multiple exciton generation (MEG; a quantum dot is a nanocrystal small enough that electronic states are discrete and Coulomb interactions are enhanced). CM is exactly the time-reverse of Auger recombination, in which an electron-hole pair recombines by transferring the energy to a third carrier instead of emitting light — so any material change that strengthens impact ionization tends to strengthen the Auger loss channel as well; this reciprocity is the crux of the problem. Thermodynamic limits for ideal CM cells far exceed single-junction values: the source chapter of this problem (Martin A. Green, 'Multiple Electron-Hole Pairs per Photon', ch. 7 of Third Generation Photovoltaics: Advanced Solar Energy Conversion) reports 85.9% for fully concentrated direct light and 43.6% for diffuse light, following the detailed-balance line of Werner, Kolodinski and Queisser and of Brendel, Werner and Queisser. In bulk semiconductors the measured effect was tiny: the best silicon cells showed IQE below 1.05 at 350 nm where 3 is energetically allowed, because phonon cooling outcompetes impact ionization. Würfel argued from hot-carrier thermodynamics that exploiting impact ionization requires hot-carrier populations and that strong electron-phonon interaction therefore precludes practical benefit; Green countered that hot carriers are not strictly necessary, deriving the limits from a generalized staircase emission analysis in which thermalized carriers emit photons through multipair channels. The ideal staircase behavior of the chapter's Fig. 7.1(b) — a step-like rise of the multipair generation at each multiple of the bandgap — requires, quantitatively, that the ratio αm+1/αm\alpha_{m+1}/\alpha_m of absorption coefficients αm\alpha_m for creating mm electron-hole pairs be large; no real alloy (e.g., SiGe) or superlattice (a periodic stack of ultrathin semiconductor layers) was known to achieve such a step-like absorption increase. The chapter also notes that 'other processes apart from impact ionisation are suggested as offering more potential for obtaining the predicted performance advantages' (p. 82). The field was subsequently transformed by colloidal quantum dots: Schaller and Klimov (2004) and Ellingson et al. (2005) reported efficient MEG in PbSe and PbS nanocrystals; a 2008-2010 controversy over conflicting quantum yields (Trinh et al. 2008 and others versus NREL measurements) was resolved by recognizing photocharging measurement artifacts, establishing that MEG is real in isolated nanocrystals with onsets approaching twice the bandgap; Semonin et al. (2011) built the first quantum-dot solar cell harvesting MEG as external photocurrent (peak external quantum efficiency — EQE, collected carriers per incident photon — of 114%); and 2019-2026 work demonstrated near-ideal CM in van der Waals transition-metal dichalcogenides (layered semiconductors such as MoTe2 and MoSe2), carrier multiplication in halide-perovskite nanocrystals (perovskites being a crystalline semiconductor family widely used in thin-film photovoltaics), and direct evidence of CM in the topological insulator Bi2Se3 (a material that is insulating in its interior but hosts conducting surface states). What remains missing, exactly as the source chapter anticipated, is a demonstrated net efficiency gain in a practical converter.

Problem Statement

Can semiconductor materials be engineered so that the generation of multiple electron-hole pairs per photon yields a practically useful quantum-efficiency and conversion-efficiency gain in a photovoltaic converter — that is, can the competing relaxation processes, hot-carrier cooling by phonon emission and Auger recombination (the microscopic time-reverse of impact ionization), be suppressed or out-competed in a real material system without simultaneously introducing losses that negate the gain, so that a net photocurrent or efficiency benefit over a comparable single-pair-generation baseline is demonstrated under solar illumination? This includes establishing which material systems (bulk alloys and superlattices, quantum dots, two-dimensional van der Waals semiconductors, halide perovskites, or others) can approach the ideal behavior assumed by the limiting-efficiency analyses — a multiplication onset near twice the bandgap with a large, step-like rise of the multipair quantum yield (large αm+1/αm\alpha_{m+1}/\alpha_m, where αm\alpha_m denotes the absorption coefficient for photons that create mm electron-hole pairs) — and whether mechanisms other than direct impact ionization, which the chapter notes 'are suggested as offering more potential for obtaining the predicted performance advantages' (p. 82), can convert excess photon energy into additional collectable carriers.

References

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