EQE is a quantative measurement to compare the efficiency of various solar cells. However, what is the comparision between the external quantum efficiency of oil to photovoltaics? This might be a relevant number since PV's main competitor is oil derivatives.
The external quantum efficiency is defined as
$$ \text{EQE} = \frac{\text{electrons out}}{\text{photons in}}. $$Eight photons of light of appropraite \(\nu\) are required to fix one molecule of oxygen. Glucose, \(\text{C}_{6}\text{H}_{12}\text{O}_{6}\) requires \(6\) oxygens, so \(48\) photons are required [1]. Plants have an efficiency of doing this process of between \(0.2\%\) to \(2\%\) [2].
This suggests for every photon,
$$\frac{0.02}{48}\frac{180g}{N_{A}} = 1.5\times10^{-25}, $$grams of plant material is generated. We assume no loss or energy use to any other than growing the plant. In other words, that all the chemicals of the plant are simply stored.
A U.S. Gallon, \(3.8\) L, of gasoline requires approximately \(90\) metric tons of ancient plant matter as precursor material [3]. If this is true, roughly \(2.4\times10^{7}\) grams of plant matter are needed per litre of oil, which means \(1.9\times10^{32}\) photons are required. The actual value is much more likely to be several orders of magnitude higher than this, due to losses in the plant, only a small portion of plant life becoming oil and whatever losses happen from plant to precursor material. But lets take the \( 10^{32}\) as a reasonable lower bound.
Fossil fuels are burnt at around \(40\%\) efficiency from fuel to electricity [4]. The total energy produced from one litre of gasoline is \(3.5 \times 10^{7} J\). Suggesting that \(40 \%\) of that can be converted to useful electrical input, and comparing that to the silicon band gap (\(1.1eV\)) [this is a cheat], means we can get roughly \(8 \times 10^{25}\) electrons out.
This suggests oil has a maximal \(\text{EQE}\) of gasoline of around $$ \text{EQE}_{\text{Gasoline}} = \frac{8\times 10^{25}}{2\times 10^{32}} = 0.00004 \%, $$ which is a disappointing value even for quantum dot solar cells.