text: Entropy generation and inefficiency in a PV cell is the result of photons more energetic than the band gap producing electrons with kinetic energy in addition to the potential energy provided by the band gap. Similarly, optical phonon energy in excess of the band gap generates an entropy flow in the pV cell, rather than electric power. The energy efficiency () is quantified by the ratio of the band gap and optical phonon energy, that is
  <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\begin{align}
  \eta_{\phi}=\Delta E_{e,g}/E_{p,\mathrm{O}}.
  \end{align}
  In addition this typical inefficiency, hot optical phonon populations tend to downconvert into multiple low-energy, acoustic phonon modes (whereas photons typically do not downconvert into low energy infrared waves). This efficiency () is quantified by the tendency of a hot optical phonon to downconvert rather than generate an electron-hole pair, that is
  <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\begin{align}
  \eta_{QE}=\dot{\gamma}_{e-p}^*=\frac{\dot{\gamma}_{e-p}}{\dot{\gamma}_{e-p}+\dot{\gamma}_{p-p}},
  \end{align}
  where  is the rate of generation and  is the rate of downconversion, i.e., the rate at which an optical phonon produces multiple low-energy, acoustic phonons. This provides a second entropy flow reducing the efficiency of a pV cell.
  Finally, entropy is generated in both pV and PV cells due to the inefficient separation of the generated electrons and holes. This efficiency () is limited by the Carnot efficiency given by
  <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\begin{align}
  \eta_\mathrm{C}=1-\frac{T_{pV}}{T_{p,\mathrm{O}}},
  \end{align}
  where  is the temperature of the pV cell and  is the temperature of the optical phonon population, as dictated by the Bose–Einstein statistics. This efficiency is reduced the smaller the band gap is in comparison to the thermal energy (, where  is the Boltzmann constant and  is the temperature). Indeed, the p-n junction efficiency is approximately
  <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\begin{align}
  \eta_{pn} \simeq \eta_\mathrm{C} [1-0.75\exp(-0.1\Delta E_{e,g}/k_\mathrm{B} T_\mathrm{pV})].
  \end{align}
  Thus, the overall efficiency () is
  <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\begin{align}
  \eta_\mathrm{pV} = \eta_\mathrm{C}\dot{\gamma}_{e-p}^*\frac{\Delta E_{e,g}}{E_{p,\mathrm{O}}} [1-0.75\exp(-0.1\Delta E_{e,g}/k_\mathrm{B} T_{pV})],
  \end{align}
  where the temperature independent terms become the material figure of merit (),
  <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\begin{align}
  Z_\mathrm{pV} = \dot{\gamma}_{e-p}^*\frac{\Delta E_{e,g}}{E_{p,\mathrm{O}}}.
  \end{align}
  If the band gap and optical phonon mode are resonant, and the optical phonon tends to generate electrons, the phonovoltaic cell can approach the Carnot limit as .