Nonequilibrium Theory of the Conversion Efficiency Limit of Solar Cells Including Thermalization and Extraction of Carriers

Abstract

The ideal solar cell conversion efficiency limit known as the Shockley-Queisser (SQ) limit, which is based on a detailed balance between absorption and radiation, has long been a target for solar cell researchers. While the theory for this limit uses several assumptions, the requirements in real devices have not been discussed fully. Given the current situation in which research-level cell efficiencies are approaching the SQ limit, a quantitative argument with regard to these requirements is worthwhile in terms of understanding of the remaining loss mechanisms in current devices and the device characteristics of solar cells that are operating outside the detailed balance conditions. Here we examine two basic assumptions: (1) that the photo-generated carriers lose their kinetic energy via phonon emission in a moment (fast thermalization), and (2) that the photo-generated carriers are extracted into carrier reservoirs in a moment (fast extraction). Using a model that accounts for the carrier relaxation and extraction dynamics, we reformulate the nonequilibrium theory for solar cells in a manner that covers both the equilibrium and nonequilibrium regimes. Using a simple planar solar cell as an example, we address the parameter regime in terms of the carrier extraction time and then consider where the conventional SQ theory applies and what could happen outside the applicable range.

Electron thermalization and relaxation in laser-heated nickel by few-femtosecond core-level transient absorption spectroscopy

“…Probing and harnessing the relaxation of hot carriers in metals and semiconductors are vital to the development and design of photovoltaics and photocatalysts [1][2][3][4][5][6][7], and to the understanding of mechanisms in various photoinduced phase transitions [8][9][10][11]. After photoexcitation, carriers driven out of equilibrium quickly form a thermalized hot carrier distribution within a few to tens of femtoseconds through carrier-carrier scattering, before further cooling takes place through carrier-phonon interactions at timescales ranging from hundreds of femtoseconds to picoseconds [12].…”

“…After photoexcitation, carriers driven out of equilibrium quickly form a thermalized hot carrier distribution within a few to tens of femtoseconds through carrier-carrier scattering, before further cooling takes place through carrier-phonon interactions at timescales ranging from hundreds of femtoseconds to picoseconds [12]. Although the carrier cooling process typically involves complex interactions between the electronic, phonon, and spin degrees of freedom, the dynamics can be successfully described phenomenologically by a "multitemperature model" in a wide variety of systems [1,3,5,[11][12][13][14][15]. In such a model, the electronic, vibrational, and spin degrees of freedom are regarded as individual heat reservoirs and the energy transfer between the reservoirs is governed by a set of "interaction coefficients."…”

Theory of Non-equilibrium "Hot" Carriers in Direct Band-gap Semiconductors Under Continuous Illumination

“…[37][38][39] Incorporation of the full non-equilibrium distributions in a self-consistent way along with the energy and number conservation distinguishes our work from existing formalisms that treat the non-equilibrium only within RTA. [33][34][35][36][37][38][39] Counter-intuitively, we find the NESS carrier distribution is more out-of-equilibrium (i.e., less resembles an equilibrium distribution), indicating higher density of non-thermal carriers at low illumination intensities than at high intensities 50 due to inefficient thermalization at low intensities. Consequently, the temperatures of the carriers become ill-defined at low intensities, and depend on the way the temperatures are measured.…”

“…1. We adopt the standard formulation, see Supplementary Sections S1-B and S1-D, for PL, 33,57,58 which is also consistent with the formulation of the photoexcitation (Section 2.1) considered above. To this end, we relax the requirement of the momentum conservation for the same set of reasons corresponding to the photo-excitation process.…”

“…Second, the existing theoretical studies of the steady-state HC dynamics have considered the HC relaxation and interband recombination within the relaxation time approximation (RTA) where the scattering rate is assumed to be independent of the NESS distributions. [33][34][35][36] Although the RTA makes the calculation of NESS distribution simpler, it neither conserves particle number nor energy within each band. Moreover, a constant (distribution-independent) relaxation rate may overestimate/underestimate the scattering rates, thereby misinterpreting the results.…”