Shockley–Queisser limit

Shockley–Queisser limit. The Shockley–Queisser limit is a fundamental calculation in photovoltaics that defines the maximum theoretical energy conversion efficiency for a single-junction solar cell under unconcentrated sunlight. First detailed in a seminal 1961 paper by William Shockley and Hans-Joachim Queisser, it establishes an absolute ceiling, typically around 33.7%, for such devices based on the principles of thermodynamics and semiconductor physics. This landmark work provided a critical benchmark against which all subsequent photovoltaic technology has been measured, shaping decades of research and development in the field.

Theoretical foundation

The limit is grounded in the interplay between black-body radiation from the Sun and the electronic properties of a semiconductor absorber. The solar spectrum incident on Earth is approximated as black-body radiation at the temperature of the Sun's photosphere. A key concept is the detailed balance principle, which requires that at thermal equilibrium, the rate of photon absorption must equal the rate of photon emission. The analysis considers the band gap of the semiconductor material, which determines the minimum photon energy that can be absorbed to create an electron–hole pair. Photons with energy below the band gap are not absorbed, while those above it lose their excess energy to thermalization, a process where the extra energy is converted to heat rather than electrical work.

Derivation and assumptions

The derivation by William Shockley and Hans-Joachim Queisser employs a detailed balance model for a single, ideal P–n junction. Critical assumptions include that every photon with energy above the band gap produces one electron–hole pair, and that the only recombination mechanism is radiative recombination. The cell is assumed to be at thermal equilibrium with its surroundings at room temperature, and it receives the standard AM1.5 solar spectrum. The calculation integrates the usable portion of the solar spectrum, accounting for losses from thermalization and the inability to absorb sub-band-gap photons. The open-circuit voltage is ultimately limited by the difference between the quasi-Fermi level splitting and the band gap.

Efficiency limits for single-junction cells

For a single-P–n junction cell under one-sun illumination (non-concentrated light), the maximum efficiency is calculated to be approximately 33.7%, corresponding to an optimal semiconductor band gap of about 1.34 eV. This value is specific to the AM1.5 spectrum. Materials like silicon, with a band gap of 1.1 eV, have a theoretical limit near 29%. Gallium arsenide, with a band gap closer to the optimum, approaches 33%. The limit decreases if non-radiative recombination processes, such as Auger recombination or recombination via Shockley–Read–Hall centers, are significant. Under maximum concentration of sunlight, where the étendue is matched, the theoretical limit increases to about 41%.

Implications for photovoltaic technology

The Shockley–Queisser limit established a clear performance target and explained why early silicon cells plateaued well below 30% efficiency. It framed the primary research challenge in photovoltaics as overcoming inherent spectral losses. This understanding guided the development of the global photovoltaic industry and influenced funding priorities at institutions like the National Renewable Energy Laboratory. The limit also underscored the economic trade-offs in material choice, as the cost of near-optimum materials like gallium arsenide often outweighed efficiency gains for large-scale deployment, cementing silicon's dominance in the commercial market.

Strategies to exceed the limit

To surpass the single-junction ceiling, advanced concepts aim to mitigate the spectral losses it identifies. Multi-junction solar cells, or tandem cells, stack materials with different band gaps, such as gallium indium phosphide and gallium arsenide, to capture a broader range of the solar spectrum; these have achieved efficiencies over 47% in laboratories like the Fraunhofer Society. Photon upconversion and downconversion schemes manipulate photon energies to better match the absorber band gap. Hot-carrier solar cells attempt to extract electron–hole pairs before thermalization occurs, while intermediate band solar cells introduce additional energy levels within the band gap to utilize sub-band-gap photons. Perovskite solar cell research often focuses on their utility in efficient tandem cell architectures with silicon. Category:Photovoltaics Category:Solid-state physics Category:Scientific theories