10.2.1
usually referred to as the Shockley–Queisser (SQ) limit, as they where the first ones to
formulate this limit based purely on physical assumptions and without using empirically
determined constants [27]. We will derive the SQ limit in a two-step approach. First, we
will discuss the losses due to spectral mismatch. Secondly, we will also take into account
that the solar cell will have a temperature different from 0 K which means that it emits
electromagnetic radiation according to Planck’s law. Just like William B. Shockley (1910–
1989) and Hans-Joachim Queisser (1931–), we will do this with the detailed balance
approach.
Spectral mismatch
There are two principal losses that strongly reduce the energy conversion efficiency of
single-junction solar cells. As discussed in Chapter 8, an important part of a solar cell is
the absorber layer, in which the photons of the incident radiation are efficiently absorbed
resulting in a creation of electron-hole pairs. In most cases, the absorber layer is formed by
a semiconductor material, which we characterise by its bandgap energy E G . In principle,
only photons with energy higher than the bandgap energy of the absorber can generate
electron-hole pairs. Since the electrons and holes tend to occupy energy levels at the
bottom of the conduction band and the top of the valence band, respectively, the extra
energy that the electron-hole pairs receive from the photons is released as heat into the
semiconductor lattice in the thermalization process. Photons with energy lower than the
bandgap energy of the absorber are in principle not absorbed and cannot generate electronhole pairs. Therefore these photons are not involved in the energy conversion process. The
non-absorption of photons carrying less energy than the semiconductor band gap and the
excess energy of photons, larger than the bandgap, are the two main losses in the energy
conversion process using solar cells. Both of these losses are thus related to the spectral
mismatch between the energy distribution of photons in the solar spectrum and the
bandgap of a semiconductor material.
Shockley and Queisser call the efficiency that is obtained when taking the spectral
mismatch losses into account the ultimate efficiency, given according to the hypothesis
that ‘each photon with energy greater than hν G produces one electronic charge q at a
voltage of V G = hν G /e’ [27].
Let us now determine the fraction of energy of the incident radiation spectrum that is
absorbed by a single-junction solar cell. If we denote λ G as the wavelength of photons that
corresponds to the bandgap energy of the absorber of the solar cell, only the photons with
λ ≤ λ G are absorbed. The fraction p abs of the incident power that is absorbed by a solar cell
and used for energy conversion can be expressed as
usually referred to as the Shockley–Queisser (SQ) limit, as they where the first ones to
formulate this limit based purely on physical assumptions and without using empirically
determined constants [27]. We will derive the SQ limit in a two-step approach. First, we
will discuss the losses due to spectral mismatch. Secondly, we will also take into account
that the solar cell will have a temperature different from 0 K which means that it emits
electromagnetic radiation according to Planck’s law. Just like William B. Shockley (1910–
1989) and Hans-Joachim Queisser (1931–), we will do this with the detailed balance
approach.
Spectral mismatch
There are two principal losses that strongly reduce the energy conversion efficiency of
single-junction solar cells. As discussed in Chapter 8, an important part of a solar cell is
the absorber layer, in which the photons of the incident radiation are efficiently absorbed
resulting in a creation of electron-hole pairs. In most cases, the absorber layer is formed by
a semiconductor material, which we characterise by its bandgap energy E G . In principle,
only photons with energy higher than the bandgap energy of the absorber can generate
electron-hole pairs. Since the electrons and holes tend to occupy energy levels at the
bottom of the conduction band and the top of the valence band, respectively, the extra
energy that the electron-hole pairs receive from the photons is released as heat into the
semiconductor lattice in the thermalization process. Photons with energy lower than the
bandgap energy of the absorber are in principle not absorbed and cannot generate electronhole pairs. Therefore these photons are not involved in the energy conversion process. The
non-absorption of photons carrying less energy than the semiconductor band gap and the
excess energy of photons, larger than the bandgap, are the two main losses in the energy
conversion process using solar cells. Both of these losses are thus related to the spectral
mismatch between the energy distribution of photons in the solar spectrum and the
bandgap of a semiconductor material.
Shockley and Queisser call the efficiency that is obtained when taking the spectral
mismatch losses into account the ultimate efficiency, given according to the hypothesis
that ‘each photon with energy greater than hν G produces one electronic charge q at a
voltage of V G = hν G /e’ [27].
Let us now determine the fraction of energy of the incident radiation spectrum that is
absorbed by a single-junction solar cell. If we denote λ G as the wavelength of photons that
corresponds to the bandgap energy of the absorber of the solar cell, only the photons with
λ ≤ λ G are absorbed. The fraction p abs of the incident power that is absorbed by a solar cell
and used for energy conversion can be expressed as