Electrothermal Feedback and Absorption-Induced Open-Circuit-Voltage Turnover in Solar Cells

Solar panels easily heat up upon intense solar radiation due to excess energy dissipation of the absorbed photons or by nonradiative recombination of charge carriers. Still, photoinduced self-heating is often ignored when characterizing lab-sized samples. For light-intensity-dependent measurements of the open-circuit voltage (Suns-$V_{\mathrm{O}\mathrm{C}}$), allowing us to characterize the recombination mechanism, sample heating is often not considered, although almost 100% of the absorbed energy is converted into heat. Here, we show that the frequently observed stagnation or even decrease in $V_{\text{OC}}$ at increasingly high light intensities can be explained by considering an effective electrothermal feedback between the recombination current and the open-circuit voltage. Our analytical model fully explains the experimental data for various solar-cell technologies, comprising conventional inorganic semiconductors as well as organic and perovskite materials. Furthermore, the model can be exploited to determine the ideality factor, the effective gap, and the temperature rise from a single Suns-$V_{\text{OC}}$ measurement at ambient conditions.

Figure 1

Suns-$V_{\text{OC}}$ measurement of an organic solar cell based on a F4-ZnPc:${\mathrm{C}}_{60}$ blend and an area of $6.44{\mathrm{mm}}^2$ for different ambient temperatures (colored squares) from 223 to 333 K in steps of 10 K. Using a global fitting routine according to Eq. (1), it is possible to determine the activation energy $E_a$. Black circles present a Suns-$V_{\text{OC}}$ measurement taken at ambient temperatures using a brighter illumination source. At high light intensities, saturation of $V_{\text{OC}}$ and a turnover is observed.

Figure 2

Suns-$V_{\text{OC}}$ measurements of (a) organic solar cell comprising a blend of DCV5T as donor and ${\mathrm{C}}_{60}$ as acceptor material; (b) organic solar cell with F4-ZnPc as donor and ${\mathrm{C}}_{60}$ as acceptor; (c) silicon photo diode; (d) perovskite solar cell. Red circles show a voltage turnover which can be explained by absorption-induced self-heating. For comparison, blue squares depict a measurement with a cooldown time between each data point with reduced electrothermal feedback. The latter lay closer to the isothermal curve.

Figure 3

Dependence of the open-circuit voltage as a function of time for various intensities for (a) the F4-ZnPc:${\mathrm{C}}_{60}$ sample and (b) for the perovskite sample. Because of self-heating and a consequential increase of the cell temperature, $V_{\text{OC}}$ decreases over time. The blue and red dashed lines mark the point in time at which $V_{\text{OC}}$ is measured in the pulsed and continuous Suns-$V_{\text{OC}}$ measurement, respectively.

Figure 4

Schematic illustration of the self-heating model. The black dotted lines show the isothermal behavior for different temperatures. All curves meet in the point ($I_{00}$, $E_a/q$). Adding absorption-induced self-heating results in deviations from the isothermal curves (red lines), i.e., the voltage decreases with increasing self-heating coefficient ${\mathrm{\Theta }}_{\mathrm{th}}^{*}$. The turnover points ${\mathrm{TOP}}_{1,2}$ (orange and purple dashed line) exists for ${\mathrm{\Theta }}_{\mathrm{th}}^{*}>e^2{T}_{\mathrm{amb}}/I_{00}$; their dependence on ${\mathrm{\Theta }}_{\mathrm{th}}^{*}$ and $T_{\mathrm{amb}}$ are shown in the Supplemental Material, part V [20].