Numerical optimisation and recombination effects on the vertical-tunnel-junction (VTJ) GaAs solar cell up to 10,000 suns

Rúa Jenaro de la Fuente, s/n –Campus Vida – Universidade de Santiago de Compostela -15782 Santiago de Compostela – citius.usc.es © 2020 International Solar Energy Society. Published by Elsevier Ltd. This manuscript version is made available under the CC-BY-NC-ND 4.0 license Numerical optimisation and recombination effects on the vertical-tunnel-junction (VTJ) GaAs solar cell up to 10,000 suns Celia Outes, Eduardo F. Fernández, Natalia Seoane, Florencia Almonacid and Antonio J. García-Loureiro Version: accepted article Celia Outes, Eduardo F. Fernández, Natalia Seoane, Florencia Almonacid and Antonio J. García-Loureiro (2020) Numerical optimisation and recombination effects on the vertical-tunnel-junction (VTJ) GaAs solar cell up to 10,000 suns. Solar Energy, 203, 136 - 144. Doi: https://doi.org/10.1016/j.solener.2020.04.029 How to cite: Copyright information: 1 Numerical optimisation and recombination 1 effects on the vertical-tunnel-junction (VTJ) GaAs 2 solar cell up to 10000 suns 3 4 Celia Outes1*, Eduardo F. Fernández1**, Natalia Seoane2, Florencia Almonacid1 and 5 Antonio J. García-Loureiro2 6 1Centro de Estudios Avanzados en Ciencias de la Tierra, Energía y Medio Ambiente, 7 University of Jaén, Spain 8 2Centro Singular de Investigación en Tecnoloxías Intelixentes, University of Santiago 9 de Compostela, Spain 10 11 *corresponding author: cou[email protected] 12 **corresponding author: [email protected] 13 14 Abstract. Ultra-high concentrator photovoltaic systems (UHCPV), usually referred to 15 CPV systems exceeding 1000 suns, are signalled as one of the most promising research 16 avenues to produce a new generation of high-efficiency and low-cost CPV systems. 17 However, the structure of current concentrator solar cells prevents their development 18 due to the unavoidable series resistance losses at such elevated concentration ratios. In 19 this work, we investigate the performance of the so-called vertical-tunnel-junction (VTJ), 20 recently introduced by the authors, by using advance TCAD. In particular, we carry out 21 an optimisation procedure of the key parameters that affect its performance and conduct 22 a deep investigation of the impact of the main recombination mechanisms and of sun 23 concentration up to 10000 suns. The results indicate that the performance of the novel 24 structure is not significantly affected by these two factors. A record efficiency of 32.2 % 25 at 10000 suns has been found. This represents a promising way to obtain state-of-the26 art efficiencies above 30 % for single-band-gap cells, and offers a new route towards the 27 development of competitive CPV systems operating at ultra-high concentration fluxes. 28 29 30 Keywords: vertical solar cells, series resistance, gallium arsenide (GaAs), tunnel diode, 31 concentrator photovoltaics 32 33 1. Introduction 34 35 Concentrator photovoltaic (CPV) technology, usually with concentration factors (Cratio) 36 within 300-1100 suns, has achieved the highest efficiencies (η), >40 %, among all the 37 PV technologies (Pérez-Higueras, et al., 2018). In addition, these systems have 38 demonstrated a noteworthy capacity to produce high energy yields and to reduce the 39 cost of electricity at locations with high solar energy resource (Fernández, et al., 2016; 40 Kamath, et al., 2019). However, despite the remarkable progress and high η of 41 commercial developments (i.e. >40 %, >30 % and >25 % at cell, module and system 42 levels), there are no systems yet able to compete with the prices of conventional non43 concentrating PVs (e.g. c-Si, p-Si, CdTe, CIGS, etc.). As a consequence, further efforts 44 are still needed to lower their cost and improve their performance to compete with the 45 classical flat PV technologies (Talavera, et al., 2016; Talavera, et al., 2017). In any case, 46 as is also signalled by several authors, there is still room for huge technological 47 improvements to increase the competitiveness of the technology (Wiesenfarth, et al., 48 2018). 49 2 50 Ultra-high CPV systems (UHCPV) with Cratio far above 1000 suns is considered as one 51 of the most promising research avenues to obtain high-efficiency and low-cost new 52 generation CPV systems (Algora & Rey-Stolle, 2012). This can be explained considering 53 that 1) the theoretical η of solar cells grows with Cratio and 2) the amount of expensive 54 semiconductor material is drastically reduced. Bearing this in mind, several efforts are 55 being conducted by the community to develop a) solar cells with η peaking at UH levels 56 (Ochoa, et al., 2016; Barrigón, et al., 2014; Paquette, et al., 2016), b) optical designs 57 able to reach UH levels with an adequate optical performance (Ferrer-Rodríguez, et al., 58 2016; Shanks, et al., 2018) and c) thermal mechanisms able to remove or/and exploit 59 the extreme heat waste produced by the cells at such elevated Cratio (Vossier, et al., 60 2018; Valera, et al., 2019; Rodrigo, et al., 2019). The most relevant constraint to develop 61 suitable UHCPV systems is related to the concentrator solar cells. Nowadays, CPV 62 systems are largely based on multi-junction (MJ) horizontal structures made up of 63 multiple III-V semiconductors with various energy gaps (EG) (Cotal, et al., 2009; Theristis 64 & O'Donovan, 2015). These cells incorporate only two electrical terminals, located on 65 the top and the back. Consequently, there is an unavoidable trade-off between the 66 shadowing of the front metal-grid pattern and the series resistance (Rs). This seems to 67 limit the developing of MJ cells with η peaking at UH levels no matter how the top-metal 68 pattern is designed or how much the cell area, so the current, is reduced (Paquette, et 69 al., 2016). Indeed, according to the last η tables, it has not yet been possible to develop 70 MJ cells with η peaking at Cratio > 1000 suns based on current horizontal configurations 71 (Green, 2020). This crucial drawback prevents the development of competitive UHCPV 72 systems. 73 74 Vertical-multi-junction (VMJ) cells offer a straightforward solution to eliminate the Rs 75 limitations of current architectures. These cells consist of a series connection of multiple 76 subcells with the metallic contacts located on the laterals (Xing, 2013; Segev & Kribus, 77 2013; Gover & Stella, 1974). This way, it is possible to develop cells with low current 78 densities, due to the large cross section of the current, and low Rs values, and therefore, 79 to develop cells optimised for UH fluxes (Sater & Sater, 2002), (Tyukhov & Vasilev, 80 1995). On the other hand, nowadays, VMJ cells are limited to indirect band-gap materials 81 with high carrier diffusion lengths (L), around 100-300 µm (Pozner, et al., 2011). This 82 limitation is imposed by the fact that direct band-gap materials present much lower L, 83 usually 1-5 µm. This would imply the series connection of approximately 200-1000 VMJ 84 cells for achieving a solar cell side of 1 mm by using lateral metallic contacts. This 85 manufacturing constraint is verified considering that, to the date, only silicon (Si) based 86 VMJ solar cells have been developed (Xing, et al., 2015). Consequently, it is not possible 87 to select the most convenient semiconductor materials to optimise the absorption of the 88 spectrum. So, although the low Rs does not limit the performance of VMJ cells with Cratio, 89 the poor semiconductor selection prevents the development of high-efficiency multi90 band-gap structures with an optimal absorption of the spectral irradiance (Braun, et al., 91 2012). 92 93 This work is focused on the optimisation and detailed performance evaluation of a novel 94 vertical solar cell structure recently introduced by the authors in a short 95 communication (Fernández, et al., 2019). This early design opened the way to 96 either use direct or indirect band-gap semiconductors. Hence, it is possible to 97 select the appropriate E G for each particular application. In the present 98 investigation, we carry out an optimisation procedure of the key parameters in 99 order to investigate the expected maximum η of the new structure for the case of 100 a single-band structure. In addition, we conduct a deep investigation of the effect 101 of the main recombination mechanisms and C ratio on the performance of the 102 device. The results of this work are fundamental to fully understand and evaluate 103 the potential of this promising device to produce a new generation of competitive 104 3 CPV systems operating at state-of-the-art concentration factors. Bearing this in 105 mind, this paper represents one of the first efforts towards the design of a novel 106 ultra-efficient concentrator solar cell, which is expected to serve as a key guideline 107 for future work concerning its manufacturing and characterization. 108 109 This paper is organized as follows. In section 2, the structure of the device under 110 consideration is described, and the simulation procedure used presented. After 111 that, in section 3, the recombination mechanisms under scrutiny are briefly 112 introduced. The optimisation of the solar cell investigated is discussed in section 113 4, and the numerical results of this optimised design presented in section 5. 114 Finally, the main conclusions are summarized in section 6. 115 116 2. Device structure and simulation technique 117 118 The device investigated in this article is an optimisation of a novel structure 119 recently proposed by the authors based on gallium arsenide (GaAs) (Fernández, 120 et al., 2019). The elementary unit of the so-called vertical-tunnel-junction (VTJ) 121 cell is made up of two identical subcells, with four layers each one, joined by a 122 tunnel junction (TJ), as shown in Fig. 1. As in our early investigation, gallium 123 arsenide (GaAs) has also been considered due to its ability for achieving high 124 conversion efficiencies. In this structure, the anode and cathode are placed 125 laterally. It is also worth mentioning that, as in our previous design, it is possible 126 to increase the area of the cell exposed to the light by connecting multiple VTJs 127 using TJs. In this sense, it is important to note that cell sides ≈< 0.5 mm are 128 desirable for developing UHCPV systems in order to facilitate the heat dissipation 129 and to reduce the cell-to-module losses (Ritou, et al., 2018). These low cell areas 130 are also key to limit the number of TJs of the total VTJ structure in order to facilitate 131 the fabrication of the device. 132 133 At this stage, the width and doping values of the p+ and n+-layers remain fixed during the 134 whole study because these layers were adjusted to the width and doping of the tunnel 135 junction. The TJ consists of a GaAs n+/p+ structure, both layers having a 25 nm width 136 and a doping of 7·1019 cm-3. This element has been simulated by including direct and 137 trap-assisted tunnelling models, as previously used by other authors (García, et al., 138 2012). Regarding the p+ and n+-layers, they have a 0.07 μm width and constant doping 139 value of 5 ⋅ 1019 cm-3. The width and doping of the p and n layers will be optimised in the 140 next section for a specific Cratio of 4000 suns. This Cratio has been considered since recent 141 investigations indicate the feasibility to develop UHCPV modules with sufficient optical 142 and thermal performance at Cratio around this value (Shanks, et al., 2018; Ferrer143 Rodriguez, et al., 2020). These layers have been selected in the optimisation procedure 144 since our preliminary simulations have proven that they are the most relevant to increase 145 the final η of the device. 146 4 147 148 Figure 1: 2D scheme of the VTJ solar cell structure (W: width and H: height). 149 150 To obtain the results, Poisson, continuity equations, which relate the electrostatic 151 potential and the carrier densities, were solved using Silvaco Atlas (Silvaco, n.d.). This 152 software is suitable due to its realistic and trustable results for the design and 153 improvement of electronic devices such as multi-bandgap concentrator solar cells 154 (Michael & Bates, 2005). 155 156 The optimisation procedure has been carried out considering Concentrator Standard 157 Test Conditions (CSTC), i.e. 1000 W/m2, AM1.5D reference spectrum, and a 25 ºC (298 158 K) cell temperature (IEC62670-1:2013, 2013). The structure is illuminated 159 perpendicularly to the PN junctions. The contacts are considered ideal, and we do not 160 account for reflections because the incoming light is parallel to the contacts. The former 161 approximation can be justified considering the low resistance of the contacts, typically 162 ranging from around 10-5 to 10-7 Ω ⋅ cm2 (Braun, et al., 2012), and the low current flow 163 of the device due to its vertical configuration. All the simulations are done in 2D because 164 we assume that the changes in the third dimension are negligible. Note that heat effects 165 are also not considered at this stage. This is due to the fact that the main intention of this 166 work is to investigate the performance of the new device as a function of Cratio. In any 167 case, future studies will be focused on the thermal behaviour of the novel structure. As 168 previously commented, the solar cell has been optimised for a Cratio of 4000 suns. 169 However, the Cratio has been varied from 1 to 10000 suns in order to evaluate the device 170 in a wide operating condition range. 171 172 It is worth mentioning that, at this stage, a VTJ cell only made up of GaAs, including the 173 TJs, has been considered. This avoids any problem of mismatching in the structure and 174 reduces the complexity of the fabrication process, i.e. the structure is lattice-matched 175 and could be monolithically grown. The intention is to propose an architecture as simple 176 as possible to facilitate future work concerning its manufacturing. In addition, this is key 177 to reduce the interface recombination effects among the different layers since the cell is 178 made up of the same material. In any case, future work should also investigate additional 179 layers such as anti-reflective coatings (ARC) or thin Al layers between the PN junctions, 180 which have already shown promising results in Si-based VMJ cells (Tyukhov, 1996). In 181 addition, despite the manufacturing is out of the scope of this paper, further comments 182 regarding its feasibility are also given. The manufacturing of the new device seems 183 possible considering the high accuracy of the growth techniques used in conventional 184 MJ solar cells nowadays, the small cell areas needed, and the electronic devices recently 185 developed based on the multiple connection of around 20 PN junctions by using TJs 186 5 (York, et al., 2018). Moreover, the lateral metallic contacts could also be placed on the 187 structure using the same methodology than in current MJ cells. This can be explained 188 considering that the total width of the final VTJ cell, ≈ 0.5 mm, and the height of current 189 MJ cells is similar, ≈ 0.2 mm (Theristis & O'Donovan, 2015). 190 191 192 3. Recombination models 193 194 In this work, we studied the main recombination effects, namely: Auger (RAuger), 195 Shockley–Read–Hall (SRH) (RSRH) and optical generation/radiative (Rrad). These 196 different effects and the total recombination (Rtotal) are related by the following equation: 197 198 Rtotal=RAuger+RSRH+Rrad . (1) 199 200 If we consider that R= 1 τ, the equation (1) can be expressed as (2) in terms of the lifetime 201 (τ), obtaining a total effective lifetime (τeff) as follows: 202 203 1 τeff =1 τAuger +1 τSRH +1 τrad . (2) 204 205 A brief description of the recombination effects considered in this work is given in the 206 next sub-sections. This is intended to facilitate the understanding of the results of the 207 present investigation. 208 209 3.1. Auger 210 211 In this recombination process, an electron and hole recombine but a photon is not 212 emitted. The energy is given to another electron, which is excited to a higher energy 213 level. Then, this electron returns to the conduction band due to thermal losses 214 (Selberherr, 1984). This model is important at high current densities and high carrier 215 concentrations such as the produced at UH levels. The standard Auger recombination is 216 modelled by the following expression (Dziewor & Schmid, 1977): 217 218 RAuger=AUGn(pn2-nnie 2)+AUGp(np2-pnie 2) , (3) 219 220 where n and p are the electron and hole concentration respectively, nie 2 the intrinsic 221 concentration, and AUGn and AUGp are, respectively, the Auger coefficients for 222 electrons and holes. 223 224 3.2. Shockley-Read–Hall 225 226 In SRH, a carrier that is in transition between the bands is trapped by an energy state 227 created by a defect or by a dopant, called trap. Then the energy is exchanged by 228 phonons. This process is dominant in indirect bandgap materials, but it can also 229 dominate in direct bandgap semiconductors if there are many traps. In our simulations, 230 we used the SRH concentration dependent lifetime model because τ also depends on 231 the impurity concentration (Roulston, et al., 1982), (Law, et al., 1991), (Fossum & Lee, 232 1982). Based on this, the SRH recombination is modelled by the following equation, 233 (Hall, n.d.): 234 235 RSRH=pn-nie 2 τp[n+nieexp(Etrap kTL)]+τn[p+nieexp(-Etrap kTL)] , (4) 236 237 6 being 238 239 τn=τn0 1+(Ntotal NSRHn) , (5) 240 241 τp=τp0 1+(Ntotal NSRHp) , (6) 242 243 where Etrap is the difference between the trap energy level and the intrinsic Fermi level, 244 TL the lattice temperature (in Kelvin), k the Boltzmann constant, τn0 and τp0 the electron 245 and hole lifetimes, respectively, Ntotal the total impurity concentration, and NSRHn and 246 NSRHp specify the SRH concentration parameter for electrons and holes, respectively. 247 248 3.3. Optical generation/Radiative recombination 249 250 In this mechanism, the photon transition has to be considered for 251 generation/recombination processes. It is a direct mechanism because occurs in one 252 step. In the radiative recombination, an electron loses energy and moves from the 253 conduction to the valence band emitting a photon with an energy similar to the gap. In 254 the optical generation, an electron moves from the valence to the conduction band. The 255 radiative recombination is the dominant recombination mechanism in direct gap 256 materials, like GaAs, and in narrow gap semiconductors. However, in indirect gap 257 materials this process is very low and then negligible. This model is also called band to 258 band recombination and can be described by equation (7), which means that the total 259 band to band generation/recombination is the difference of the capture rate and emission 260 rate processes: 261 262 Rnp OPT=CC OPT(np-nie 2) , (7) 263 264 where CC OPT means the capture rate. 265 266 The parameters considered to take into account the mechanisms above are listed in 267 Table 1. 268 269 nie 2.67 · 106 cm-3 (Grundman, n.d.) , (Vurgaftman, et al., 2001) AUGn 5 · 10-30 cm6/s (Picozzi, et al., 2002) AUGp 1 · 10-31 cm6/s (Govoni, et al., 2011) Etrap 0 eV (Silvaco, n.d.) τn0 4.4 · 10-4 s (Lush, et al., 1992) τp0 2.2 · 10-4 s (Schubert, 2006) NSRHn,p 2.7 · 1013 cm-3 (Silvaco, n.d.) CC OPT 1.5 · 10-10 cm3/s (Olson, et al., 1989) 270 Table 1: Recombination parameters used in the numerical simulations. 271 272 273 4. Optimisation procedure at 4000 suns concentration 274 275 In this section the optimisation of the structure shown in Fig. 1 for a Cratio of 4000 suns is 276 presented. First, the optimisation of the height, by changing its value to maximize the η, 277 was carried out. At this stage, the width and doping values of each layer of our previous 278 7 work were considered. An optimum height value of 15 µm was found. Once the height is 279 selected, the width and doping of the n and p layers have been analysed. First, these 280 values were varied for the p-layer while the n-layer parameters were kept constant at 2.5 281 µm and 1⋅1015 cm-3. Finally, the n-layer parameters were also optimised by following the 282 same procedure. In this case, the p-layer parameters were kept constant at 5 µm and 283 1⋅1015 cm-3. The initial values of each layer to perform the optimisation have been 284 selected based on the structure of the VTJ presented in our previous work. 285 286 Figure 2: Contour plot of the efficiency as a function of the width and doping of the p287 layer (left) and n-layer (right) of the VTJ optimisation at 4000 suns. 288 289 290 Fig. 2 shows the η dependence with the doping and the width for the two layers 291 optimised. As can be seen, for the p-layer (Fig. 2 (left)), η increases as the doping 292 decreases. A maximum η of 31.7 % has been found. This value corresponds to a width 293 ranging from 4.2 to 6.6 µm, and a doping ranging from 1⋅1015 to 3⋅1015 cm-3. On the 294 other hand, for the n-layer (Fig. 2 (right)), η also increases as the doping decreases. A 295 maximum η of 31.7 % was obtained for width values between 2.0 and 4.0 µm, and doping 296 values between 1⋅1015 and 2⋅1015 cm-3. Based on this study, the width of the p-layer has 297 been considered equal to 6.0 µm, and 3.0 µm for the n-layer. In addition, a doping of 298 1⋅1015 cm-3 has been considered for both layers. With this configuration, the maximum 299 η, i.e. 31.7 %, for the highest width has been achieved. The latter is crucial to maximize 300 the area of the cell, and therefore to decrease the number of TJs as much as possible 301 for structures based on the tunnelling connection of multiple VTJ cells. 302 303 As can be also seen in Fig. 2, η is more sensitive to the width and doping variations in 304 the n-layer (η varies from 25.8 % to 31.7 %) than in the p-layer (η varies less than 1 %). 305 This can be understood considering the different electron and hole mobilities (µ) for the 306 layers and their relation with the L, i.e. the higher the µ the higher the L (Markvart & 307 Castañer, 2005). In the p-layer, Fig. 2 (left), the n minority carriers have a higher µ, which 308 implies a better carrier collection in the electrodes. As a consequence, the short-circuit 309 current (ISC), and therefore η, are less sensitive to the width and doping variations. This 310 can be understood considering that η is proportional to ISC: 311 312 η= ISC VOCFF Pin = Pmax Pin , (8) 313 314 where VOC the open-circuit voltage, FF the Fill Factor, and Pin and Pmax are the incident 315 and maximum power output, respectively. On the other hand, in the n-layer, Fig. 2 (right), 316 the p minority carriers have a lower µ. Hence, the carrier collection in the electrodes is 317 8 lower than in the previous case. As a consequence, the ISC, so the η, are more sensitive 318 under the width and doping variations. 319 320 In addition to the effects above, the different carrier concentration between the two layers 321 also contributes to enhance their different behaviour under width and doping variations. 322 The n-layer has more carriers, so, the recombination effects in this layer become more 323 relevant, being the radiative and SRH recombination mechanisms the most affected (see 324 section 5). These rates increase with the number of carriers, as can be obtained from 325 the analysis of the equations (4) and (7), and therefore the τeff tends to decrease. As in 326 the previous case, this contributes to reduce L, and therefore η is more affected under 327 the width and doping variations in this layer. 328 329 330 331 Figure 3: Comparison of the efficiency between the VTJ of this work (Fig. 1) and the 332 structure of our previous work (Fernández, et al., 2019). 333 334 Fig. 3 shows a comparison of the η between the optimised structure of this work and the 335 results of our previous design for Cratio ranging from 1 to 10000 suns. As can be seen, 336 the optimised design strongly improves the η. These η values are around 4 % higher 337 than in the previous design except for Cratio of 1 sun, which is around 3 % higher. The 338 optimisation procedure conducted in this section allows solar cells with record η above 339 30 % at ultra-high concentration factors to be developed. 340 341 342 5. Numerical results 343 344 In this section, first, the effect of the different recombination mechanisms and their total 345 effect on the VOC, ISC and Pmax at 4000 suns have been studied. After that, the main 346 recombination mechanisms and their impact on the key electrical parameters as a 347 function of Cratio have been investigated. 348 349 5.1. Impact of recombination 350 351 First, the effect of the Auger, radiative, SRH and their combined total recombination in 352 the VOC point was analysed, under a Cratio of 4000 suns. The different recombination 353 15 11 present the IV curves, and key electrical parameters, for three different recombination 534 scenarios (only radiative, only SRH and all recombinations) at 100 suns and 4000 suns, 535 respectively. For a Cratio of 100 suns the VOC for the SRH case is around 2.4 % higher 536 than that of all recombinations. However, the Pmax of the SRH recombination only grows 537 by 1.9 %. As consequence the FF decreases in a larger extend since this is given by: 538 539 FF= Pmax ISC· VOC . (10) 540 541 On the other hand, for a Cratio of 4000 suns, the VOC for the SRH case is also higher, 542 around 2.2 %, than that of all recombinations. However, in this case, the Pmax grows 543 around 3.3 %. As consequence, the FF becomes higher than the value when all the 544 effects are considered. 545 546 The phenomenon above could be explained by analysing the saturation current (I0) for 547 the different cases. This value has been extracted by using the Phang model (Phang, 548 et al., 1984), also previously validated to investigate concentrator solar cells by the 549 authors (Fernández, et al., 2016). At 100 suns, the SRH is the main contributor to the all 550 recombinations and presents a I0 value three orders of magnitude larger, I0 =1.50 10-19 551 A, with regards to the only radiative, I0 = 6.75 10-22 A. This high value of I0 degrades the 552 IV curve in a larger extend and could explain the smaller increase of the Pmax respect to 553 the VOC. It is also important to mention that the higher VOC values of the SRH case are 554 due to a higher m value previously estimated, m (radiative) = 1.00 while m (SRH) = 1.12. 555 However, at a higher Cratio of 4000 suns, radiative is the main recombination effect, the 556 I0 is around eight times larger, I0 = 8.38 10-20 A, with respect to the only SRH, which is 557 1.14 10-20 A. In addition, the I0 for the SRH case is lower than that at 100 suns. As a 558 consequence, the IV is less affected and could also explain why Pmax grows in larger 559 extent than VOC, and therefore, why the FF is higher at UH Cratio with respect to the all 560 recombination case. 561 562 563 Figure 10: I-V curves and some electrical parameters for the only radiative, only SRH 564 and all recombinations case with a Cratio of 100 suns. 565 566 567 568 16 569 Figure 11: I-V curves and some electrical parameters for the only radiative, only SRH 570 and all recombinations case with a Cratio of 4000 suns. 571 572 573 Figure 12: Efficiency as a function of Cratio for the VTJ solar cell without recombinations, 574 for each recombination and for all recombinations. 575 576 Fig. 12 presents the η as a function of the Cratio for the VTJ solar cell, showing both the 577 individual contributions of the three analysed recombination effects (Auger, radiative and 578 SRH), and their combined effects (all recombinations). As previously, it was also 579 considered the no recombinations case for comparison. It is also important to mention 580 that Auger effects are negligible even at extreme Cratio of 10000 suns. This is relevant 581 considering that this mechanism has been previously signalled by other researchers as 582 the ultimate limiting factor to produce device valid to achieve UH levels due to the large 583 amount of carriers generated (Govoni, et al., 2011). 584 585 17 As shown in the figure, η increases almost linearly with the logarithm increase of Cratio for 586 all the cases. The small reduction of the FF previously signalled for Cratio above 2000 587 suns does not limit the performance of the device with Cratio. η varies from ≈ 25.2 % at 1 588 sun to a maximum value of ≈ 32.2 % at 10000 suns. Regarding the recombination 589 mechanisms, at low Cratio below 100 suns, the SRH and radiative recombinations 590 contribute similarly to the reduction in the η. For larger Cratio, the radiative is the dominant 591 effect and degrades the η the most. At the same time, the SRH effect becomes 592 insignificant as the Cratio increases. It was also found that the reduction of η due to all 593 recombination contributions is higher at UH irradiances (1.4 % at 10000 suns) than at 594 low irradiances (1.1 % at 1 sun). This is due to the fact that the radiative mechanism 595 dominates as the Cratio is increased. Hence, the small reduction in the FF introduced by 596 this mechanism with the Cratio, see Fig. 9, also contributes to degrade the η to a greater 597 amount, see also equation (8). 598 599 Despite of the above, the η achieved by the optimised VTJ cell would represent a record 600 η solar cell, which is nowadays 29.3 % for a GaAs conventional structure at a Cratio ≈ 50 601 suns (Green, et al., 2018), far below the solar concentration levels here investigated. 602 This represents a promising route to deliver single-band-gap structures with state-of-the603 art η > 30 % due to the elimination of the series resistance constraints. 604 605 606 607 6. Conclusions 608 609 In this work, we have studied a novel structure based on gallium arsenide (GaAs) 610 previously proposed by the authors in a short communication. This structure was 611 optimised at a concentration ratio (Cratio) of 4000 suns in order to improve the device 612 efficiency (η). Once the device was optimised, the effect of the different recombination 613 mechanisms and their total effect on the open-circuit voltage (VOC), short-circuit current 614 (ISC) and the maximum power (Pmax) was studied along the width of the vertical-tunnel615 junction (VTJ) structure. Finally, the impact of the main recombination mechanisms on 616 the key electrical parameters as a function of Cratio was investigated. 617 618 For this structure, it was carried out an optimisation of the device height and the width 619 and doping of the p and n layers. As a result of this procedure, a maximum η value of 620 31.7 % for a Cratio of 4000 suns was demonstrated. This significantly improves the η of 621 our previous design by a value ranging from 3 % to 4 % for all the Cratio analysed. 622 623 For this solar cell, the radiative recombination is the dominant mechanism. For the VOC, 624 this mechanism is around 97.3 % of the total recombination. For the Pmax, it is around the 625 88.0 % (at a 3 µm cutline along the width of the VTJ structure). Nevertheless, at the ISC 626 point, the radiative recombination is 63.8 % and 55.9 % of the total recombination for the 627 p and n-layers respectively, whereas the SRH recombination is 36.2 % (p-layers) and 628 44.0 % (n-layers) of the total recombination (at a 3 µm cutline). These recombination 629 rates decreased as we moved away from the surface where the light was falling on. It 630 was found Auger recombination was almost negligible for all the parameters. 631 632 In addition, our study indicated that the behaviour of the key electrical parameters was 633 not limited by neither of the recombination mechanisms. The ISC grew linearly with the 634 Cratio independently of the recombination mechanism considered and it is not affected by 635 neither of them. The VOC also increased linearly with the logarithm of the Cratio. It was 636 found that the all recombination effects lowered this magnitude less at extreme 637 concentrations (2.1 % at 10000 suns) than a low Cratio (3.5 % at 1 sun) with respect to 638 the ideal case. Results also showed that at Cratio above 100 suns the dominant 639 mechanism was radiative recombination, whereas at low Cratio the radiative and SRH 640 18 contributions were similar. For the Fill Factor (FF), it was found that for all recombination 641 case it grew up to 2000 suns and then decreased with the logarithm of Cratio. The 642 maximum FF value obtained was 88.53 % at 2000 suns. Above this Cratio, the FF slightly 643 decreased, obtaining a value of 87.95 % for 10000 suns. 644 645 Results showed a linear increase in the η of the VTJ solar cell with Cratio and no 646 remarkable impact (maximum observed η degradation of 1.37 % at 10000 suns respect 647 the ideal case) caused by the recombination mechanism investigated. For Cratio<100 648 suns the SRH and radiative recombinations contributed similarly to the η reduction, 649 whereas for Cratio>100 suns the radiative recombination dominated and degraded the η 650 the most. A maximum η of 32.2 % at 10000 suns was obtained. This would represent a 651 record η, being currently a 29.3 % for GaAs conventional structures at a Cratio of 50 suns, 652 at Cratio far above any previous solar cell found in the literature. This highlights the interest 653 and potential of the vertical solar cell here investigated to produce a new type of structure 654 tailored to achieve extreme Cratio. 655 656 Future work should investigate the performance of the cell under temperature, spectrum 657 and uniformity variations. In addition, structures made up of different materials and/or 658 with additional layers, such as anti-reflective coatings (ARC), should be considered in 659 order to enhance the potential efficiency of the device. Finally, the investigation of multi660 band-gap structures made up of several VTJs aimed to optimise the absorption of the 661 spectrum should be the topic of further investigations. This could be achieved by 662 mechanically stacking multiple VTJ solar cells made up of different materials and energy 663 gaps on the top of each other in decreasing order of the band-gap. 664 665 666 Acknowledgement 667 668 E. F. Fernández and F. Almonacid thank the Spanish Economy Ministry and FEDER 669 funds received under the project ENE2016-78251-R. N. Seoane and A. J. García 670 Loureiro thank Spanish Ministry of Economy and Competitiveness and FEDER funds 671 (TIN2016-76373-P) and the Xunta de Galicia and FEDER funds (GRC 2014/008). N. 672 Seoane and E.F. Fernández also thank the Spanish Ministry of Science, Innovation and 673 Universities (RYC-2017-23312, RYC-2017-21910). C. 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