Scope of the study Photoconversion efficiency

Scope of the study Introduction Much effort has recently been directed towards increasing efficiency η of multi junction solar cells (MJSCs). MJSCs have shown promise for increasing photoconversion efficiency; therefore realistic optimization of MJSCs, given fundamental constraints on photoconversion, is important to provide achievable efficiency targets for both research labs and industry. However, standard theoretical formalisms of photoconversion are not comprehensive enough to realistically reproduce experimental efficiencies. Photoconversion efficiency η of multijunction solar cells (MJSCs) under AM1.5 has reached 38.8% and 44.4% under concentrated illumination [1]. However, currently there is a gap between the experimental approaches to develop MJSCs, and often idealized formalisms to model their efficiency. The vast majority of existing computational work is performed based on thermodynamic Carnot approach or energy balance model (see, for example, [2] - [4]). Only one paper introduces such parameters as saturation currents for radiative recombination and Shockley-Read-Hall (SRH) recombination [5]. In the photoconversion model of [5] processes of light re-radiation and re-absorption (photon recycling) in the structures with multiple reflections were considered, resulting in open circuit voltage VOC increase. Recombination contribution to the photoconversion processes from radiative recombination and Shockley-Read-Hall recombination were also introduced in. Meanwhile, to accurately and realistically predict efficiencies of experimentally produced MJSCs and optimize their parameters, photoconversion models must consider (i) radiative lifetime τr, SRH lifetime τSR, recombination in the space charge region (SCR) and surface recombination velocity S, (ii) optimal base and emitter doping levels, as well as their thickness, and (iii) selfconsistent balance between the MJSC temperature and efficiency. Since MJSCs contain multiple homo or hetero-junctions, trade-offs between interfaces and thin film contributions are also important in the photoconversion processes, but they also were not sufficiently addressed. To overcome the above mentioned limitations we develop a new semi-analytical self consistent approach to calculate photoconversion efficiency for MJSCs with both vertical and lateral design and apply the formalism to MJSC under AM0 and AM1.5 illuminations. In addition to radiative recombination, both Shockley-Read-Hall and interface recombinations (using typical values for direct bandgap III-V semiconductors) were included into the approach. We show that for the typical lifetime of order 10-8 s, which semiconductor technologies offer for A3B5 compounds based MJSCs, the contribution of the light re-absorption and re-emission to the photoconversion efficiency can be neglected. In our simulation of the efficiency a balance between η and the MJSC temperature T is self consistently treated. With increase of subcell number n, the difference between the band gap and photon energies as well as the MJSC temperature decrease. This effect increases open circuit voltage VOC and efficiency η and should be particularly strong for solar cells in space applications. In the outer space the solar cell temperature is not limited by reasonably high temperature of the environment such as in terrestrial application. Furthermore, it is demonstrated in self consistent way that the MJSC temperature strongly depends on the properties of heat sink that removes excessive heat from the MJSC. Our formalism accounts for decrease of the emitted heat and operating MJSC temperature when the number of current matched subcells n increases. Increase of n narrows the spectral range for each subcell, additionally reducing the photocurrent due to energy dependent light absorption, and this fundamental limitation is ignored in other approaches Scope of the study The study is focused on the Photoconversion efficiency of quantum-well solar cells for the optimum doping level of a base, how it affects development of the state, country or areas. It will also involve the analysis of problems associated with Photoconversion efficiency of a place. Aims and Objective of the study The broad objective of the research is to evaluate the impact created by Photoconversion efficiency of quantum-well solar cells For the optimum doping level of a base The other aims and objective of this study includes: i. To determine the level of modern light generation ii. To find out the level of photocoversion efficiency on light and fluorescent. iii. To determine the importance solar cells and quantum well on photoconversion efficiency. Disadvantages as an optical marker The tetramerization of Kaede may disturb the localization and trafficking of fusion proteins. This limits the usefulness of Kaede as a fusion protein tag. ANALYSIS Since the solar spectrum that reaches subcells of MJSC and being adsorbed is in the 0.3m < λ < 2m wavelengths range, non-photoactive low energy photons with λ > 2m do not contribute to the SC temperature increase. For simplicity of our analysis, we consider here the recombination losses only, and in such a case it follows from Eg. (20) that η(n) = η0(n). Processes of re-absorption of light are considered in [5] are important if the nonradiative recombination can be neglected. When calculating VOC in this case, instead of the radiative recombination parameter A we have to use Aeff=A(1-γr) with γr the photon re-emission factor. This increases the efficiency, and when we calculated η, the reflection coefficient Rd was put to zero. In contrast, when the nonradiative recombination is present, η change due to the re-absorption can usually be neglected [8]. In this paper, rather than relying on reabsorption processes, the MJSC efficiency gain is achieved mainly by improving heat dissipation. This can be done by increasing the MJSC emissivity parameter β, making this as close to blackbody as possible. If the solar cell heat dissipates through the top illuminated surface, β is close to 0.9 [11]. By blackening the back surface of the MJSC, the emissivity parameter can be increased to ~1.8. Another method of improving the heat dissipation is to use radiator fins, where the heat emission occurs from larger area than the area of the illuminated MJSC surface (KT >1). We also analyze the influence of the subcells’ base doping level n0 on MJSC photoconversion efficiency η. When the Shockley-Read-Hall recombination dominates, η reaches maximum at n0 = 1017cm-3. For the n-type base the maximum of η is due to interplay of both Auger recombination and Burstein- Moss effect, with the last decreasing the light absorption coefficient near the absorption edge. For the p-type base, Burstein- Moss effect does not contribute to the maximum of efficiency happening. The above considerations are used to optimize n0 when simulating MJSC efficiency η. We first calculate η(n) for the hypothetical model system when each subcell is made of a direct-gap III-V semiconductor with exact energy gaps Egi, always available to satisfy current matching. The following parameters were used: Aeff = 2⋅10‐10 cm3/s , D = 50 cm3/s, Nc= 5⋅1017 cm-3, Nv= 1019 cm-3. We also considered d = 2 ⋅10-4 cm, dp = 10-6 cm, τp = 10-10 s, n0 = 1017 cm-3, Ss = 103 cm/s and δ = 10-2 W/sm2⋅K. The surface recombination velocities and the Shockley-Read lifetimes considered to be the same for each subcells of MJSC. When SRH recombination is considered, we use τSR = 5 ⋅ 10-9 s. Here, Rd=0 and β =1.5, while the heat dissipation conditions are varied: curve 3 KT=1, curve 2 KT=5, and curve 3 corresponds to a forced cooling with MJSC temperature T=300K, which produces the highest η. Curve 4 describes the experimentally achieved efficiencies for different numbers of subcells in MJSC. The figure demonstrates reasonably good agreement of our theoretical results with experimentally available efficiencies. It is important to stress that for improved heat sink, for instance, with γ = 6 ⋅ 10-3 W/cm2⋅K at AM1.5 MJSC temperature increases only slightly above the ambient temperature, thus resulting into to the efficiency close to that one at ambient temperature. SUMMARY In this paper we propose modified efficient semi-analytical approach to realistically calculate the photoconversion efficiency η(n) for multijunction solar cells, applicable for both terrestrial and space applications, and using concentrated or non-concentrated light. The formalism incorporates important mechanisms of photogenerated carriers’ losses due to Shockley- Read-Hall bulk recombination, space charge layer recombination as well as surface recombination at the illuminated and back MJSC surfaces, and heterojunction interfaces respectively. The above recombination contributions reduce the efficiency η compared to the case when only radiative recombination dominates. MJSC efficiency η(n) has been calculated first for the hypothetical “ideal” system when each subcell is made of a direct-gap III-V semiconductor with exact energy gap Egi, required to satisfy current matching. With efficient heat sink and increasing subcells number n, calculated maximum MJSC efficiencies can exceed 60% for AM0 conditions and 50% for AM1.5. RECOMMENDATION In recommendation the, approach described in this paper are that we considered more realistic conditions when SRH recombination dominates over the radiative recombination. This corresponds to, for instance, AM1.5 conditions.