Energy Conversion Efficiency of the Bulk Photovoltaic Effect

The bulk photovoltaic effect (BPVE) leads to directed photocurrents and photovoltages in bulk materials. Unlike photovoltages in $p$-$n$ junction solar cells that are limited by carrier recombination to values below the band-gap energy of the absorbing material, BPVE photovoltages have been shown to greatly exceed the band-gap energy. Therefore, the BPVE is not subject to the Shockley-Queisser limit for sunlight to electricity conversion in single-junction solar cells and experimental claims of efficiencies beyond this limit have been made. Here, we show that BPVE energy conversion efficiencies are, in practice, orders of magnitude below the Shockley-Queisser limit of single-junction solar cells and are subject to different, more stringent limits. The name BPVE stands for two different fundamental effects: the shift current and the injection current. In both of these, the voltage bias necessary to produce electrical energy accelerates both intrinsic and photogenerated carriers. We discuss how energy conservation alone fundamentally limits the BPVE to a band-gap-dependent value that exceeds the Shockley-Queisser limit only for very small band gaps. Yet, small band-gap materials have a large number of intrinsic carriers, leading to high conductivity that suppresses the photovoltage. We discuss further how slightly more stringent fundamental limits for injection (ballistic) currents may be derived from the trade-off between high resistivity, needed for a high voltage, and long ballistic transport length, needed for a high current. We also explain how erroneous experimental and theoretical claims of high efficiency have arisen. Finally, we calculate the energy conversion efficiency for an example two-dimensional (2D) material that has been suggested as a candidate material for high-efficiency BPVE-based solar cells and show that the efficiency is very similar to the efficiency of known 3D materials.

Popular Summary

The bulk photovoltaic effect (BPVE), a second-order nonlinear effect that converts light into electricity in solids, has attracted a great deal of interest for power conversion applications and it has been assumed that BPVE can lead to more efficient solar cells. However, the overall efficiency of such devices should be comprehensively understood. Here, formulation of the energy conversion efficiency limits for the BPVE conversion mechanism show that the limits are more stringent than the single $p$-$n$ junction limit. In fact, practical efficiencies remain very low, orders of magnitude below those of $p$-$n$ junction solar cells.

Figure 1

An illustration of the current in a device made of a bulk semiconductor and two electrodes at the sides of the device. The average shift of the charges (electrons and holes) per absorption event of the incoming light (green arrows) is denoted as $R$. This shift may occur due to ballistic transport or due to the shift vector.

Figure 2

(a) Circuit diagram of a BPVE cell showing the current source $I_{\mathrm{sc}}$ and parallel resistors $R_{\mathrm{dark}}$ and $R_{\mathrm{ph}}$, representing the dark conductivity, proportional to the intrinsic carrier density, and the photoconductivity, proportional to the photoexcited carrier density, respectively. (b) A resulting linear $I$-$V$ curve with short-circuit current $I_{\mathrm{sc}}$, open-circuit voltage $V_{\mathrm{oc}}$, and maximal extractable electrical power $P_{\mathrm{el}}$, illustrating the fill factor of $25\mathrm{\%}$.

Figure 3

Zero-temperature broadband limit of solar energy conversion with the injection current. The area labeled ${\mathrm{PV}}_{0\mathrm{K}},E_{\mathrm{pot}}\to Q$ describes the power that an ideal single-junction photovoltaic device operated at 0 K could produce (in a mechanical analogy it could be seen as the potential energy of the carriers in the conduction band). The area labeled “Transparency loss” describes the loss through photons that are not absorbed by the device. The area labeled $E_{\mathrm{kin}}\to Q$ describes the part of the kinetic energy of the photoexcited carriers that cannot be converted to electrical power and is converted to heat, while the area labeled $E_{\mathrm{kin}}\to P_{\mathrm{el}}$ describes the electrical power that would be extracted by an ideal bulk photovoltaic with perfect excitation asymmetry.

Figure 4

Room-temperature efficiency limit for solar energy conversion, assuming that the asymmetry of injected carriers is perfect ($\zeta =1$) and assuming different effective electron masses $m_e$ at the band edge. The hole effective mass is set to $m_h=1$. The Shockley-Queisser (SQ) limit is shown for comparison.

Figure 5

Frequency-dependent (a) photoresponsivity, (b) average shift vector, and (c) absorptivity of 2D $\mathrm{Ge}\mathrm{Se}$. Frequency-dependent (d) photoresponsivity, (e) average shift vector, and (c) absorptivity of a 2D semi-Dirac material.