肖克利-奎塞尔极限

The Shockley–Queisser (SQ) limit, also known as the detailed balance limit, provides a foundational ceiling on the energy conversion efficiency of solar cells. It is derived by analyzing the 热力学 balance between the energy absorbed from the sun and the energy lost by the cell. The model makes several key assumptions: the cell is a single p-n junction, it operates at a standard temperature (300 K), and it is illuminated by unconcentrated sunlight (AM1.5G spectrum).

The calculation accounts for several unavoidable loss mechanisms. First, photons with energy less than the semiconductor’s bandgap ([latex]E_g[/latex]) pass through the cell without being absorbed, contributing nothing to the current. Second, for photons with energy greater than the bandgap, the excess energy ([latex]E_{photon} – E_g[/latex]) is quickly lost as heat through thermalization, as the excited electron relaxes to the bottom of the conduction band. The voltage is thus limited by the bandgap, not the photon energy. The most significant loss mechanism considered in the SQ limit is radiative recombination. This is the reverse process of absorption, where an electron and hole recombine and emit a photon. In an ideal cell, this is the only recombination pathway. The cell, being at a non-zero temperature, also radiates energy as a black body.

By balancing the incoming photon flux from the sun with the outgoing flux from radiative recombination and black-body radiation, Shockley and Queisser derived the current-voltage characteristic of an ideal cell. The maximum power point on this curve defines the maximum efficiency. The efficiency is a strong function of the bandgap energy, peaking at ~33.7% for a bandgap of 1.34 eV, which is close to that of Gallium Arsenide (GaAs). For silicon ([latex]E_g \approx 1.12[/latex] eV), the limit is around 32%.