Ultraviolet radiation impact on the efficiency of commercial crystalline silicon-based photovoltaics: A theoretical thermal-electrical study in realistic device architectures

We investigate and evaluate the contribution of the ultraviolet radiation spectrum on the temperature and efficiency of commercial crystalline silicon-based photovoltaics (PVs) that operate outdoors. The investigation is performed by employing a comprehensive thermal-electrical modeling approach which takes into account all the major processes affected by the temperature variation in the photovoltaic devices. We show that effectively reflecting the ultraviolet radiation (i.e. up to a certain wavelength) results in a reduction of the overall operation temperature and enhancement of the PV cell's efficiency. In addition, blocking the high energy ultraviolet photons prolongs the life time of the PV and its performance on the long term.

hand and the increase of the temperature on the other hand (due to the high thermalization losses in the cell and the high parasitic absorption from EVA encapsulant that is located on top of the cell).
In this respect, in the present study, we consider realistic commercial crystalline silicon PVs (dominant in the market of solar cell technology [9]) and evaluate in detail the total impact of the UV radiation on the PV efficiency. For this evaluation we employ a comprehensive thermalelectrical co-model (described in detail in Perrakis et al. [10]) which calculates the solar cell steady state temperature (for given incident power, materials and weather conditions) as well as its efficiency as a function of temperature taking into account all the major processes affected by the temperature variation in a commercial PV device. These processes include the material-dependent radiative and non-radiative recombination of electron-hole pairs (such as the temperature-dependent nonradiative Auger recombination process), which have been identified as the major cause for the voltage decline and the subsequent efficiency decrease of PVs operating at elevated temperatures [10].
The model-PV system employed in the present study is a state-of-the-art silicon-based PV module [8,11] (see Fig. 1a), where the active layer (within the cell) is of crystalline silicon, basically a p-n homojunction diode (silicon bandgap ~1.107μm). The cell is placed in-between two EVA layers while a top glass layer is used to protect the cell and offer more stability. (The system is described in more detail in Fig. 1a, while the material parameters for its different materials are obtained from Ref. [10]). In this system we explore the impact of the UV radiation by gradually reflecting it (by 100%), starting from a wavelength equal to 0.28 μm -where the highest thermalization losses occur, up to a given wavelength λr, and calculating the output electrical power or efficiency with respect to the operating temperature (T) at typical outdoor conditions. (As a positive "side effect", directly reflecting UV radiation instead of utilizing UV absorbers results to a reduced overall system temperature.) More specifically, our modelling approach [10] integrates (i) full-wave electromagnetic simulations (using the commercially available software CST Microwave Studio), to calculate the absorptivity/emissivity of the PV at the thermal mid-IR wavelengths (4-33 μm) (with a 5 o angular resolution), and a (ii) thermal and (iii) electrical part. The full-wave calculated emissivity data are imported into the thermal part of our analysis, which associated to the reflection of the incident UV radiation for the system of (a), for a reflection wavelength range from 0.28 μm to λr. For all cases the ambient temperature is equal to 298 K. To mimic typical outdoor conditions, we assume an irradiance level (Irrl) of 40% (of the "AM 1.5G" standard sunlight spectrum [12]) and a combined nonradiative heat transfer coefficient, hc, equal to 20 W/m2/K (black lines), Irrl=100%, hc=20 W/m2/K (blue lines), and Irrl =100%, hc=10.6 W/m2/K (red lines). The green dashed line in (c) indicates the EVA absorption. The two black/red dashed vertical lines correspond to two different λr of 0.363/0.37 μm and 0.375/0.393 μm where we observe the maximum efficiency improvement and the limiting point where the efficiency remains unharmed for the conditions of the black/red curve case. The orange and blue filled areas in (b) and (c) correspond to the normalized "AM1.5G" standard sunlight spectral irradiance and photon flux respectively.
utilizes the passive radiative cooling approach that was firstly proposed by Fan [13] to calculate the steady state temperature of the device. The approach balances the power "into" and "out of" the device. The power "into" the device is the power absorbed from the solar emission, noted as Psun, which is directly affected by any elimination of UV part, and the power absorbed from the atmosphere, Patm(Tamb), where Tamb is the ambient temperature. The power "out of" the device is connected with the thermal radiation, Prad,PV, the non-thermal radiation, Prad, cell, which corresponds to the radiation emitted through electron-hole recombination [14], the nonradiative heat transfer (Pcond+conv=hc(T-Tamb), hc is the nonradiative heat transfer coefficient) and the output electrical power (Pele, max). The above are summarized in the following relation: Since in our case the operating temperature of the device is greater than the ambient temperature, Tamb, the nonradiative heat transfer (due to the convection and the conduction taking place within the device and its interface with the environment) is a heat dissipation out of the device, offering an additional cooling effect besides radiative cooling. The electrical part utilizes the Detailed Balance Principle described by Shockley and Queisser [15] to calculate the current (J) -voltage (V) characteristics of the cell for a given temperature (and through them the power Pele,max, plugged-in also in Equation (1)). In applying this principle, besides the losses due to radiative electron-hole recombination, we additionally take into consideration the fundamental temperature dependent non-radiative-Auger recombination loss [16]. In this respect, the efficiency, η, of a commercial crystalline silicon PV which operates at its maximum power (mp) point is given by where Pinc is the incident power. The efficiency is self-consistently determined as we combine the electrical and the thermal part and solve the steady-state problem, i.e., when the power balance equals to zero [(Pnet,cool(Vmp,T)=0 see Equation (1)] [10,13]. The above described approach (detailed in Ref. [10]), which allows to calculate the impact of any part of the electromagnetic spectrum on the PV efficiency, is employed below for the examination of the UV reflection impact on the efficiency and operating temperature of the realistic PV module shown in Fig. 1a operating at outdoor conditions. Figures 1b and 1c depict the impact on the PV temperature change (Fig. 1b) and on the PV efficiency (Fig. 1c) of totally reflecting the solar energy from 0.28 μm to a parameter wavelength λr, as λr varies from 0.28 μm to 0.45 μm, i.e. covers all the emitted by the sun UV radiation. For the temperature and efficiency calculations we assumed that the PV is operating at outdoor conditions, with Tamb=298 K. To capture the effect of the variant environmental conditions we assume three different cases, (i) an irradiance level (Irrl) of 40% (of the "AM 1.5G" standard sunlight spectrum [12]) and a combined conduction-convection nonradiative heat transfer coefficient, hc, equal to 20 W/m 2 /K (black curves), a value corresponding to strong wind climates, (ii) Irrl =100%, hc=20 W/m 2 /K (blue curves), and (iii) Irrl =100%, hc=10.6 W/m 2 /K (red curves), i.e. weak wind climates. The orange and blue areas in Fig. 1b and Fig. 1c respectively correspond to the normalized "AM1.5G" standard sunlight spectral irradiance and photon flux respectively and the green dashed curve in Fig. 1c indicates the EVA absorption.
As seen in Fig. 1b, reflecting incident radiation leads always to a temperature reduction (compared to the primary PV, i.e. without UV reflection), as is expected. Interestingly though, we found that the reflection of the UV radiation up to a certain wavelength may lead to an increase (up to ~0.1%) rather than a decrease of the PV efficiency, despite the reduction of potential carriers. This is clearly seen in Fig. 1c and, e.g., for 0.28-0.39 μm where the efficiency change obtains positive values in the red curve case. In other words, the negative effects of high EVA absorption (shown by the green dashed line in Fig. 1c) in this regime and the thermalization losses seem to overcompensate the positive effect of the additional potential carriers generated by the UV (see blue area in Fig. 1c).
Moreover, the impact of reflecting certain UV wavelengths on the device's temperature and efficiency varies for each of the different cases due to the alteration of the environmental conditions that affect the power-temperature relation and thus the steady-state operating temperature [10]. Climates with lower wind speeds, e.g. hc <13 W/m 2 /K, are expected to allow higher cut-off wavelength λr and hence higher temperature reduction. For instance, assuming a wider reflection wavelength range, with λr =0.393 μm (see right vertical red line in Fig. 1b and Fig. 1c), the PV could operate at an up to ~2.3 K lower temperature compared to λr =0.37 μm but its performance is not sacrificed only for the hc =10.6 W/m 2 /K, Irrl =100% case (where the efficiency change remains positive as seen in Fig. 1b -red curve). In implementing a practical approach though to cut parts of the UV spectrum, given that λr can be specified only during the manufacturing procedure, it is essential to calculate a λr which will be robust in respect to the variant environmental conditions as well as the various characteristics of commercial PVs. to λr =0.363 μm (solid lines) and λr =0.375 μm (dashed-dotted lines) for ambient temperature Tamb =298 K, with respect to the nonradiative heat transfer coefficient, hc, for the system of Fig. 1a. The figures show the impact of the UV reflection for an irradiance level (Irrl) 100% (UV -red lines), and a much lower one (Irrl =40% -orange lines), and for different PV characteristics, like higher silicon thickness (W =500 μm -black lines), Tamb =313K (purple lines).
Next we calculate such a constant/fixed cut-off reflection wavelength, λr; it is calculated for Tamb=298 K, hc =20 W/m 2 /K, and a lower irradiance level (40% of the "AM 1.5G" standard sunlight spectrum [12]), which is the worst-case scenario studied (black curves of Fig. 1). Calculating λr by requiring maximum temperature reduction (without harming efficiency) we obtain λr =0.375 μm; requiring the maximum possible efficiency increase (for the above-mentioned environmental conditions) the resulting cut-off reflection wavelength is λr =0.363 μm. Figure 2 presents the impact of the UV reflection on temperature (Fig. 2a) and efficiency (Fig. 2b) for a PV operating outdoors for different, typical environmental conditions, i.e. as a function of the combined conduction-convection coefficient. The UV reflection is total reflection (i.e. 100%) in the wavelength range from 0.28 μm up to the two cut-off reflection wavelengths λr specified above (solid curves correspond to λr =0.363 μm, assumed for maximum efficiency, and dashed-dotted curves correspond to λr =0.375 μm, assumed for maximum temperature reduction). Additionally, in Fig. 2 we examine the impact of the UV reflection on the PV temperature and efficiency for thicker silicon layer (W =500 μm -black), higher Tamb (313 K -purple), and an irradiance level 100% (Irrl =100% -red) and a much lower one (Irrl =40% -orange). As seen in Fig. 2, reflecting UV radiation up to λr =0.375 μm leads to an efficiency increase by up to ~0.15% (dashed-dotted red in Fig 2b). Additionally, the temperature reduction compared to the primary PV, i.e. without UV reflection, can reach values up to ~2.2 K (dashed-dotted red in Fig 2a). Assuming a narrower reflection wavelength range (λr =0.363 μm) results to a slightly higher efficiency (compared to the λr =0.375 μm case -see solid versus dashed-dotted lines in Fig 2b) for more windy climates (hc >13 W/m 2 /K), but with slightly (up to ~0.5 K) higher operating temperature (see solid versus dashed-dotted curves in Fig 2a). Moreover, as seen in Fig. 2, the results are robust even for different PV or environment characteristics met in commercial PVs operating outdoors. Taking into account all cases, the PV operating temperature can be reduced by up to ~2.2 K (see Fig. 2a) due to the UV reflection, without decreasing the efficiency (see Fig. 2b). An even higher impact from UV reflection can be expected in PVs with high electrical-power -temperature coefficients, as well as in top contact solar cells, where there is additional parasitic absorption from the metallic top contacts (thus higher room for heat elimination), in concentrated systems, and in PVs with lower than unity internal quantum efficiencies [17] (collected carriers -absorbed photons ratio) in UV.
To demonstrate the UV-reflection impact with realistic structures we apply the theory discussed above in the case of the PV device of Fig.  1(a) covered by a realistic UV reflector, that is a one-dimensional (1D) photonic crystal (PC) -see Fig. 3(a). The proposed 1D PC consists of 45 alternating Si3N4 (ε~4) -MgF2 (ε~1.82) thin layers and was designed to effectively reflect part of the UV spectrum (i.e. reflects as close as possible to the previously presented 0.28-λr wavelengths) -see Fig. 3(b) (We note that in our study, we assume the thermal power radiated by the PV is not affected by the top thin 1D PC.).  Fig. 1(a) green line). The two black dashed vertical lines correspond to two different λr of 0.363/0.375 μm discussed in connection with Fig. 2.