## 4 Results and Discussion
This cycle is repeated again verifying reproducibility of the results. The measured decrease in the output power is around 0.4% per 1 \({}^{\circ}\)C increase in cell temperature, which is close to the theoretical values [62]. Based on these experiments, we can conclude that our measurement procedures and protocols are proper for the intended study. We now turn to the small-area multi-junction solar cell (InGaP/InGaAs/Ge triple-junction SC) and verify that the light concentration function properly. The solar cell without a heat sink was illuminated with the concentrated light corresponding to 500, 1000, 1500 and 2000 suns (see Figure 6). At the moment of switching on the illumination the open-circuit voltage, \(V_{\text{OC}}\), was 2.75, 3.15, 3.35 and 3.65 V under 500, 1000, 1500 and 2000 suns, respectively. The open-circuit voltage increases with the increasing concentration as expected. After just a few minutes of illumination, the \(V_{\text{OC}}\) value decreases by 29-34% owing to heating of the solar cell. Increasing the light concentration resulted in small linear increase in the short-circuit current. Figure 7 shows that the short-circuit current, \(I_{\text{SC}}\), increases slightly with increasing temperature (about 1%). This increase in ISC cannot compensate for the decrease in \(V_{\text{OC}}\). Overall, the current scales up with increasing the light concentration. The output  
Figure 5: Open-circuit voltage and the cell temperature as the functions of time for the multi-junction solar cell under one sun illumination. The increase in the cell temperature under illumination results in the corresponding decrease in the open-circuit voltage. power of the multi-junction solar cell decreases with time owing to the sharp drop of the open-circuit voltage. These results further demonstrate the importance of thermal management of multi-junction solar cells under highly concentrated illumination. To prevent or reduce the power loss, we attached the multi-junction solar cell to an aluminum heat sink with the graphene-enhanced TIMs. For comparison, we also run experiments for the solar cell on a heat sink without TIM and on a heat sink with commercial TIM. Figure 8 shows \(V_{\textrm{OC}}\) of the multi-junction solar cell under 1000 sun concentrated light. One can see a significant positive effect of additional graphene fillers for heat removal from the cell. The decrease in voltage becomes less than 12% when TIM with 4 wt % of graphene is used as compared to 29% decrease in the cell operating without TIM. This translates to recovery of about 60% of the power loss. Figure 9 presents results for the same type of testing but with the 2000 sun light concentration. One can see that the open-circuit voltage drop went from 0.9 V in case of 1000 sun to 1.2 V for 2000 sun concentration due to overheating. The use of the graphene enhanced TIMs allows one to decrease the \(V_{\textrm{OC}}\) degradation from 34% to about 12% of the initial value. This constitutes a recovery of about 65% of the energy lost  
Figure 6: Open-circuit voltage as the function of time for the multi-junction solar cell under concentrated illumination corresponding to 500, 1000, 1500 and 2000 suns. Figure 7: Short-circuit current as the function of time for the multi-junction solar cell under concentrated illumination corresponding to 500, 1000, 1500 and 2000 suns. due to overheating. In both cases, TIMs with graphene perform substantially better than conventional commercial TIMs. It is also important to note that improvement in TIMs performance comes at a very low loading fraction of graphene. The obtained values for reduction in the temperature of the cell and saved output power are specific for the tested multi-junction cell and depend on many parameters, e.g., the heat sink used, ambient temperature cell design, and others. The performance of graphene-enhanced TIMs with other PV cells may vary.