Solar Energy Materials & Solar Cells Impact of front-side point contact/passivation geometry on thin- ﬁ lm solar cell performance

In this work, we perform an extensive campaign of three-dimensional numerical simulations of CIGS solar cell structures to investigate the e ﬀ ect of a surface-passivated CIGS with point contacts openings on the cell performance parameters (J sc , V oc , FF and η ). Detailed analysis of the combination of passivation thickness, point contact size and pitch is performed under the hypothesis of highly defective CIGS front surface and ideal chemical passivation: e ﬃ ciencies close to the case of ideal (i.e., defect-free) CdS/CIGS interface can be achieved by optimized nanometer-scale point contact arrays. To account for ﬁ eld-e ﬀ ect passivation due to positive residual charge density, Q f , within the passivation layer, we vary Q f in the range 10 10 – 10 13 cm − 2 under the two extreme scenarios of ideal or ine ﬀ ective chemical passivation. Several examples of CIGS cells with di ﬀ erent bu ﬀ er layers (CdS, ZnO, ZnMgO, In 2 S 3 , Zn(O, S)) are also analyzed. We ﬁ nd that a positive Q f in the interval 10 12 – 5·10 12 cm − 2 can help completely recover the ideal cell e ﬃ ciency, irrespective of the chemical passivation e ﬀ ect and even in the presence of unfavorable conduction band alignment at the bu ﬀ er/CIGS heterojunction. This may help devising solutions with bu ﬀ er materials alternative to CdS, boosting the performance of otherwise surface-limited cells. The e ﬀ ect of grain boundary defect density and position with respect to point contacts is also addressed, with a grain dimension of 750 nm.


Introduction
Improvement in conversion efficiency of Cu(In 1−x Ga x )Se 2 (CIGS) solar cells has been steady and remarkable, with laboratory-scale CIGS cells reaching efficiencies above 20% on a polyimide substrate [1] and beyond 22% [2,3] on soda-lime glass, thus exceeding those of other thin-film technologies. Improving conversion efficiency is essential to foster the competitiveness of photovoltaics in the energy market, and requires that the main performance-limiting electrical and optical loss mechanisms be identified so that, in a second step, researchers and manufacturers can devise solutions to overcome these limits. Major electrical losses in the cell are non-radiative bulk and interface recombination, which are therefore among the first and foremost performance limiters to take care of.
Record cells [1][2][3] feature a CdS buffer deposited by chemical bath to ensure suitable interface quality and favorable band-alignment at the CdS/CIGS interface, which results in low recombination rate through the inversion of CIGS surface, so that the cell should be limited by bulk properties, according to [4,5]. The assumption that interface recombination does not play a major role in CIGS solar cells with CdS buffer layer is also supported by several publications discussing the transport mechanism in CIGS solar cells (e.g., [6]). Applying this interpretation to the measured values of the parameters in the one diode model will result in the conclusion that interface recombination is not dominant. However, Scheer showed that interface recombination can be still the dominant mechanism even if the measured activation energy for J 0 is equal or close to the value of the energy band gap of the absorber [7]. Furthermore, the improvements obtained with the recently introduced alkaline post deposition treatment, which affects the interface between CIGS and buffer layer, strongly support the assumption that interface recombination is still limiting the device performance [8].
At the same time the interest in Cd-free buffer layers has been continuously growing, with the twofold purpose of reducing the absorption losses in the short wavelength range caused by the relatively low optical band gap of CdS (2.4 eV), and disposing of toxic Cadmium: alternative buffer materials with higher bandgap than CdS are available (the best alternatives being the ZnO-based compounds like Zn(O,S), ZnMgO and ZnSnO and the In 2 S 3 [9][10][11][12]), but the quality of the interface with CIGS and of electron transport across the heterointerface are often insufficient to provide efficiencies higher or even comparable with those of CdS-buffer cells [13,14].
Especially in the presence of sub-optimum buffer/absorber interface, the introduction of surface passivation and point contacts might help boost the cell performance, similarly to the case of advanced PERC cells [15] in silicon solar cell technology. Rear-passivated CIGS cells have been proposed with nano-sized point contacts [16], and recently ZnS nano-dots as a passivation film in combination with In 2 S 3 point contacts have proven to be a viable strategy to improve the cell performance beyond that of simple planar In 2 S 3 buffer by reducing the region of high interface recombination [17]. With the passivation layer approach the requirements of buffer/absorber interface quality can be relaxed, provided that the passivation layer effectively reduces the defective junction and interface recombination losses.
Surface passivation can be used to suppress recombination, whereby the open circuit voltage and the efficiency can be improved. Passivation can lower recombination losses in two ways: i) by reducing the density of active interface defects, impurities or dangling bonds at the CIGS surface (chemical passivation); ii) the presence of charge inside the passivation layer can either repel minority carriers from the semiconductor interface (in the case of negative passivation charge) or enhance surface inversion of the CIGS (in the case of positive passivation charge), thus inhibiting recombination (field-effect passivation) [18]. In the case of silicon technologies, over the years different materials as silicon nitride (SiN), silicon dioxide (SiO 2 ), amorphous silicon (a-Si), and, more recently, aluminum oxide (Al 2 O 3 ) and hafnium oxide (HfO 2 ), have proven to possess both chemical and field-effect passivation qualities [19][20][21].
Among deposition methods, atomic layer deposition, ALD, has the ability to deposit ultrathin layers down to 5 nm, at the same time maintaining good passivation of the surface [19]. The passivation capability of ALD Al 2 O 3 is confirmed also when deposited on CIGS [22], probably due to the field-effect more than the reduction of defects at the surface (which is estimated at about 35%) [23]. The control of this field-effect due to charge inside the passivation layer is thus crucial to assure effective surface passivation. Even if the residual charge inside the ALD Al 2 O 3 is negative, both its magnitude and polarity can be varied from −3.5×10 12 cm -2 to +4.0×10 12 cm -2 by inserting additional layers of HfO 2 and SiO 2 [21], making this material an interesting candidate to passivate both the front and rear sides of the absorber, where positive and negative charge, respectively, is optimum for fieldeffect passivation.
As far as point contact opening is concerned, unfortunately, the conventional patterning techniques used in silicon solar cells are not applicable to chalcopyrite thin films, due to the surface roughness of the polycrystalline absorber and the shorter diffusion length of minority carriers, which requires mean size and distance of localized openings in the nanometer scale [22,24,25]. Recently, though, a novel surface nanopatterning method was presented, obtained by selfassembling of alkali condensates (SALT) [26] forming nanostructures ( < 30 nm) on the rough polycrystalline surface of chalcogenide thin films with conformal coverage, thus opening new opportunities for front interface passivation.
The evidence from all these studies suggests the importance of theoretical investigation of the passivation and point contacts geometry to understand their effects on cell performance, with the aim at overcoming the limitations induced by non-optimal interface properties. In this paper therefore we expand on a previous report [27] using three-dimensional (3D) numerical simulations to study the impact of inserting a passivation layer with point contacts at the buffer/CIGS interface. We vary the passivation layer thickness, and the point contact width and pitch, in order to determine the optimum configuration for high efficiency in the presence of highly defective buffer/ absorber and passivation/absorber interfaces. The effect of varying the doping of CdS and CIGS in combination with point contacts is also addressed. In this study, we take a closer look at the field-effect passivation induced by the density of fixed charge inside the passivation layer. We mostly focus on a standard CdS/CIGS stack, but results are extended to different buffer materials. Moreover, since the polycrystalline structure of CIGS and the presence of gran boundaries (GBs) are known to influence the cell performance significantly [28,29], although the bulk of this work is focused on single-crystal structures, we also simulate cells featuring surface passivation and contacts openings in the presence of GBs.
The ultimate goal of this work is providing cell manufacturers with guidelines for high-efficiency designs with optimized cross-sectional and layout features, and passivation layer requirements.

Materials and methods
Starting from the passivation-plus-local opening geometry achievable by the SALT technique, a picture of which is shown in Fig. 1 (left) (a detailed description of the technique can be found in [26]), we simulated the cell schematically shown in Fig. 1 (right).
The passivation layer thickness h, the point contact width wpc, and pitch d are varied in order to evaluate their effect on cell performance. When h=0, the CdS covers the whole CIGS surface, and the cell structure is the standard one (i.e., with neither passivation nor point contacts).
We modeled the cells using the Synopsys Sentaurus-Tcad suite [30], using cylindrical-symmetry 3D simulations except where otherwise noted. The cell's behavior in the dark is described by the Poisson, electron and hole continuity, and drift-diffusion equations. Recombination via deep defects follows the Shockley -Read -Hall (SRH) model. The cell is illuminated by the standard AM1.5G solar spectrum, and the light propagation through the layered media is calculated by the transfer matrix method (TMM). This model assumes ideal, flat interfaces between layers and coherent propagation, i.e., layers that are thinner than the optical coherence length. The second assumption is generally accurate enough; the first one, on the other hand, is questionable in the case of thin-film polycrystalline cells: however, since measured optical coefficients are used in the simulations, the effect of surface roughness is to some extent incorporated in the model, and TMM simulations were shown to provide good match between measured and simulated External Quantum Efficiencies (EQEs) without any fitting of optical coefficients (see for example [31]). The simulated cell has a double graded [Ga]/([Ga]+[In]) (GGI) composition of the absorber of the type described in [32], yielding a depth-dependent bandgap: the measured GGI profiles are loaded into the model of the solar cell to give the corresponding band gap profiles (as described more in detail in [31]). The optical behavior is described by complex refractive indexes coming from the literature [33] or from unpublished measured data (for CIGS), depending on both GGI and [Cu]/([Ga]+[In]) ratios. All simulations include spatially uniform bulk recombination centers in the CIGS; as far as interface recombination is concerned, we examined two scenarios for the CdS/CIGS interface: ideal interface (no trap centers), and non-ideal interface (with trap centers). While most of the simulations do not consider the presence of grain-boundaries (GBs), the effect of defect-rich GBs is considered at the end of the next section. The most significant material parameters [28,29,34] for the various cell layers are given in Table 1. The passivation is modeled as a transparent layer with Eg=5 eV, forming a conduction band spike (ΔE C =0.5 eV) at the interface with CIGS. It is worth pointing out that the exact value of the energy gap of the passivation layer used in simulation is not very relevant, since passivation is considered to be transparent. Possible candidates for cell fabrication could be HfO 2 (Eg=5.3-5.7 eV), Al 2 O 3 (Eg=6.4 eV) [35], or SiO 2 (Eg=3.9 eV), as explained later.

Chemical passivation
We started setting the baseline for the standard cell with h=0i.e., no passivationin the case of ideal CdS/CIGS interface; the simulated cell efficiency under AM1.5G illumination is 21.6%, as reported in Table 2 together with measured data from [1].
Donor-type interface states (related to (In, Ga) Cu defects), which can be converted from shallow to deep donors under photoexcitation [36] and deep bulk acceptor-type defects (related to the V Se -V Cu −/2− vacancy complex) crossing the Fermi-level very close to the interface are expected inside the CIGS [37] and are often associated with the N1 level observed in the admittance spectra and with light-and biasinduced metastabilities [38].
Starting from the ideal-case bulk-limited cell (η=21.6%), in order to simulate a case of surface-limited cell, we introduced either acceptor or donor traps with a density of 10 10 ÷10 11 cm −2 at the CdS/CIGS interface, corresponding to surface recombination velocity of 10 3 ÷10 4 cm/s. All traps are energetically located at the CIGS mid-gap: in fact, our simulations showed that the effect of both interface acceptor-like and donor-like defects is largely independent of the trap energy level as long as the latter is within ± 0.3 eV from the intrinsic Fermi level. As listed in Table 2, the lowest efficiency, η=15.9%, is obtained for acceptor defects of density N AT =10 11 cm −2 , due a larger reduction of both V oc and FF caused by enhanced surface recombination and defectinduced band bending.
In order to decouple the effect of recombination from that of band bending due to charged interface defects, we also simulated the separates cases of i) neutral recombination centers and ii) negatively charged (i.e., acceptor-type) interface defects with low enough capture cross section to make surface recombination negligible, as detailed in Table 2. As expected, the negatively charge defects affect FF (−2.7% absolute) due to a change in the band bending, leaving V oc unchanged, while the neutral recombination centers reduce V oc (−0.07 V) and, as a consequence, FF, as reported in Table 2. In the presence of acceptor traps, these two effects, namely, the different band bending due to negatively-charged acceptors and trap-assisted surface recombination, combine to reduce the cell's efficiency to the 15.9% minimum observed in Table 2.
With reference to the interface-limited cell with 10 11 cm −2 acceptors, in order to identify the optimum passivation layer thickness and Table 1 Material parameters used in the simulations.

ZnO
CdS CIGS N D : 10 20 -AZO  Table 2 Baseline (h=0) cell parameters under AM1.5G illumination. In the case of non-ideal interface cell, A (D) indicates acceptor (donor) traps. The best performance, with η=19.3%, is reached with a point contact width wpc=20 nm and closely spaced (d=50 nm) point contacts. The best efficiency obtained for each value of h and the corresponding combination of d and wpc is shown in Table 3. The complete set of the cell's figures-of-merit is shown as a function of wpc and for different values of d, in the case of h=10 nm, in Fig. 2.
Even with the optimal configuration (h=5 nm, Table 3), the efficiency recovery -about 3.4% absoluteoffered by surface passivation with point contacts does not restore the ideal bulk-limited case efficiency (η=21.6%). In fact, contrary to V oc , which completely recovers the loss due to the defective CdS/CIGS interface, the fill factor (78.1%) remains lower than that of the ideal-interface solar cell (82.1%). As shown by Fig. 2 (top right), FF is severely degraded for narrow point contacts, due to the increased resistance of the current path in the absorber and through the point contact openings, despite the carrier diffusion length being in the micrometer range for both electrons and holes. The parasitic resistance of point contacts increases with passivation thickness, too, because the CdS thickness covering the point contact cornerswhich is equal to (30 nmh), as seen in Fig. 1 is reduced for higher h.
On the other hand, Fig. 2 shows that, starting from wpc values in the low nanometer range, increasing wpc makes the cell tend toward the surface-limited case, due to insufficient passivation of the interface defects. The performance degradation for increasing wpc can be expected to be gentler for less defective interfaces. This means that the success of the passivation-with-point-contacts strategy depends on the trade-off between the beneficial effect of surface defects passivation, which is maximum for narrow point contacts and wide pitch, and the detrimental effect of series resistance, which is aggravated when the point contacts are narrower and wider apart.
Since the series resistance introduced by the passivation layer with point contacts is the factor limiting the cell performance, we evaluated the effect of increasing the doping densities. It can be expected that the more conductive the CIGS and CdS layers, the less will the cell suffer from series resistance effects, thus enhancing the benefit of point contacts. With reference to a cell with h=10 nm, d=50 nm, wpc=10 nm, we have thus simulated the illuminated behavior for different values of the CIGS acceptor doping density keeping the CdS donor doping density fixed at 2×10 16 cm −3 , and similarly for different values of CdS donor doping keeping the CIGS acceptor density fixed at 1×10 16 cm −3 , as shown in Fig. 3. While increasing the CdS doping (Fig. 3, black line) does prove successful owing to reduction of the parasitic series resistance of the point contact path and improved band alignment [39], higher CIGS doping (Fig. 3, orange line) lowers the FF due to an unfavorable combination of doping and band alignment, as detailed in [27,39]. In both cases, the effect of increased doping is marginal on V oc and J sc , and FF controls the cell performance.
The presence of passivation on top of the CIGS makes the CdS redundant outside of the point contact areas, and suggests the possibility of removing the CdS everywhere except in the point contacts, thus increasing the photon inflow and the External Quantum Efficiency (EQE). Thus, we chose the cell with h=10 nm, wpc=10 nm, d=50 nm, and removed the CdS from the passivation top, leaving everything else unchanged. The simulated efficiency improves from 18.4% to 21.0%, not only due the expected reduction of absorption losses in the CdS (corresponding to a J sc increase of +1 mA/cm 2 ), but also to the improvement of FF (+7% absolute), the latter mainly attributed to the series resistance (extracted from the slopes of the I-V curve near V oc ) decreasing from 3.10 to 1.55 Ω cm 2 when the CdS is removed from the top of the passivation layer and is replaced by more conductive ZnO.

Field-effect passivation
In the previous analysis we assumed perfect passivation of interface defects, that is, defect-free passivation-layer/absorber interface. In that case the passivation with point contact arrangement allows to recover the cell efficiency significantly, but not so much as to attain the bulklimited η=21.6%. An other cause that may lower recombination at the CIGS surface is the reduction of the density of one type of carrier by means of the electric field induced by the charge within the passivation. A positive charge, attracting electrons at the surface, favors the photocurrent flow and moves the CIGS surface deeper into inversion thus reducing the recombination. In order to evaluate this effect, we consider the presence of a fixed positive charge density, Q f , inside the passivation layer, which is varied in the range 10 10 -10 13 cm −2 . Positive Q f are reported in HfO 2 layers [20], in SiO 2 /HfO 2 /Al 2 O 3 stacks depending on the thicknesses of different materials [21], or in asdeposited Al 2 O 3 [40].
We examined two scenarios for the case of the most detrimental acceptor traps density, N AT =10 11 cm −2 (see Table 1 for defect properties): i) the acceptor traps are present only at the buffer/absorber interface, i.e., only in the point contact openings, which corresponds to ideal chemical passivation at the absorber/passivation interface, and ii) acceptor traps are present all over the CIGS surface, which instead simulates the opposite case of ineffective chemical passivation.
As shown in Fig. 4, even with ideal chemical passivation of defects (red triangles), the efficiency is shown to improve by almost 3.6% absolute in the case of additional field-effect passivation induced by positive Q f mainly by the increase of FF, slightly surpassing the bulklimited cell with no passivation (reference dotted line in Fig. 4). In fact, the positive Q f reduces the barrier seen by photo-generated electrons leaving the absorber, as shown in in Fig. 5a for V=0.4 V (corresponding to the Maximum Power Point, MPP, in the case of Q f =0 cm −2 ), and also favors the accumulation of electrons at the inverted passivation/ absorber interface (Fig. 5b) thereby reducing the resistance of the current path inside the absorber: consequently, FF increases and so does efficiency. Not surprisingly, the benefit of field-effect passivation is even larger in the case of inefficient chemical passivation of defects: the 12.5% efficiency obtained with Q f =0 jumps to 21.9%, if positive Q f > 5· 10 11 cm −2 is present at the passivation/absorber interface (Fig. 4,  circles).
The efficiency improvement is due to the increase of both V oc (+180 mV) and FF (+18% absolute), respectively originating from the inhibition of recombination and the improved band alignment at the CIGS surface. The presence of field-effect passivation helps relaxing the requirements on point contact size: in the presence of positive fixed charge density Q f =10 12 cm −2 , local openings through the passivation in the range 5-20 nm practically give the same cell efficiency, as shown in Fig. 6.

Alternative (non-CdS) buffer layers
In order to evaluate the effectiveness of field-effect passivation in combination with buffer materials alternative to CdS, we simulated the front contact nanostructured CIGS-based solar cell of Fig. 1 (h=10 nm,  d=50 nm, wpc=10 nm), with several buffer materials alternative to CdS. We considered the same values of layer thicknesses, doping levels, and recombination rates used for the cell with CdS of Fig. 1, mainly focusing on the effect of the different conduction band offsets (CBOs) at the hetero-interfaces. The CBOs at the ZnO/buffer and buffer/CIGS interfaces used in our simulations come from the literature and are summarized in Table 4 together with the simulated cell figures of merit for the two cases of Q f =0 (no field-effect passivation) and Q f =1-5· 10 12 cm −2 (optimum field-effect passivation). In both cases, no chemical passivation of defects is considered at the passivation/CIGS interface. For the Zn 1−x Mg x O, we considered the case of low Mg concentration (x=0. 19), as previous studies [41] showed that larger x necessitates nearly degenerate or degenerate Zn 1−x Mg x O to achieve good efficiency. The optical complex refractive indexes of the studied buffer materials   4. Simulated cell parameters vs. fixed charge density inside the passivation layer with h=10 nm, wpc=10 nm, d=50 nm for the two scenarios of acceptor interface states with density 10 11 cm −2 i) at point contact only (triangles) and ii) all over the CIGS surface (circles). The reference line indicates the case of absence of interface states and passivation (i.e., reference cell in Table 2). come from the literature (for In 2 S 3 ) [42], from unpublished measured data (for Zn 0.81 Mg 0.19 O), or are the same as for ZnO (for the Zn(O,S)).
3.1.3.1. CBO CIGS/Buffer > 0. As the data in Fig. 7 demonstrate, in these cases (CdS, Zn(O, S), Zn 0.81 Mg 0.19 O), a positive Q f ≥10 12 cm −2 is sufficient to hinder recombination at the defective CIGS surface for all studied materials, boosting V oc (symbols) irrespective of the conduction-band offset value at the buffer/absorber hetero-junction. Moreover, the concentration of electrons, which are majority carriers at the inverted passivation/CIGS interface, is raised by the positive charge and the barrier seen by photo-generated electrons leaving the absorber   Table 2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Table 4
Simulated cell performance data with and without field-effect passivation, for different buffer materials (h=10 nm, wpc=10 nm, d=50 nm) in the case of acceptor interface states (N AT =10 11 cm −2 ) at point contacts and passivation/absorber interface. No chemical passivation of defects is assumed at the passivation/CIGS interface. Negative (positive) CBO indicates a cliff (spike).  is reduced (see Fig. 5b), so that the FF monotonically increases with Q f . The combination of the two factors leads the efficiency (bars in Fig. 7) up to and beyond 21.6%.

CBO CIGS/Buffer < 0.
In the presence of a cliff at the buffer/CIGS interface (In 2 S 3 /ZnO), the barrier to the flow of photo-generated electrons from the absorber to the buffer layer is removed, as shown by conduction band diagram of ZnO-buffered cell depicted in Fig. 8a, and FF is higher than that of CBO CIGS/Buffer > 0 case, even when Q f =0, and increases further with positive Q f due to the increased bandbending under the point-contact (Fig. 8a) and passivation (Fig. 8b), the latter mainly reducing the series resistance of the current path.
As the positive Q f increases, the downward band-bending of the conduction band enhances the interface acceptor trap ionization and at the same time repels holes (minority carriers) at the surface: the competing effects of increased inversion (hindering recombination) and enhanced trap ionization (promoting recombination) determine the non-monotonic V oc dependence on the fixed charge density, as shown by data in Table 5. The high V oc and FF when Q f =0 combine to give the 19% efficiency of the ZnO/i-ZnO/CIGS stack (19.9% for ZnO/i-ZnO/In 2 S 3 /CIGS). In the case of ZnO (In 2 S 3 ) buffer, the minimum V oc is reached for Q f =10 12 cm −2 , beyond which the electric field induced by Q f is high enough to push away the holes from the CIGS surface; the recombination decreases again and V oc starts to increase like for the other buffer materials boosting the efficiency to 22.3% for ZnO and 21.6% for In 2 S 3 .

Poly-crystalline cell simulation
Even if polycrystalline CIGS solar cells have reached efficiencies up to 22.6% [2], the presence of grain boundaries (GBs) is detrimental to the efficiency, as shown in many studies [28,29,49,50]; therefore, we analyzed the effect of the presence of GBs in a cell with passivation and contact openings, as shown in Fig. 9.
In this case, due to the great number of grid points required to model such a wide area with the necessary resolution and the absence of the cylindrical symmetry of the structure in Fig. 1, we performed 2D simulations (as opposed to the 3D simulations described so far). Even if the simulated contact openings represent line contacts rather than point contacts, the simulation study can give an indication of the effects of GB in the presence of a nanostructured CIGS front surface. In order to simulate a realistic structure, we considered a grain size of 750 nm containing 15 line contacts with 50 nm pitch, and wpc=10 nm. We also varied the distance t of the GB relative to contact center (t=0 and 20 nm). Thanks to symmetry, we modeled only half of the structure in Fig. 9, for the two cases where the GB lies i) exactly in the middle of at the contact opening (as shown in Fig. 9), or ii) midway between neighboring point contacts. We considered the case of ideal chemical passivation of defects (i.e., defects at point contact only) and no fieldeffect passivation (i.e, Q f =0).
The GB is modeled by a 2 nm wide region rich with donor traps [28,51] (see Table 1 for GB trap parameters): we considered both the cases of high (N T =10 13 cm −2 , which corresponds to 5·10 19 cm −3 ) and  low (N T =10 11 cm −2 , which corresponds to 5·10 17 cm −3 ) defect density inside GBs. Besides the different defect population, the GB differs from the grain interior (GI), by a larger bandgap due to Cu depletion; the band discontinuity is entirely in the valance band, and we assumed ΔΕv (GB/GI) =0.15 eV [52][53][54].
In the presence of the most defective GBs (type I in Tables 1 and 6), the cell efficiency is reduced by about 1%, mainly by the drop of FF, while the GB position relative to the contact center does not affect the obtained results. So, there appears to be no significant interaction of GBs with the passivation and point contact scheme, and the singlecrystal results shown above can be considered to be representative.

Conclusions
This work details the application of 3D numerical simulation to the optimization of CIGS solar cells with passivated buffer/absorber interface and front-side point contacts. The effects of both chemical and field-effect passivation are analyzed in the case of CdS as well as alternative buffer materials.
We found that, in the presence of surface-limited performancei.e., with strongly defective buffer/CIGS interfacethe use of surface passivation in combination with point contacts can help the cell recover most of the performance loss due to interface states, provided that the passivation is effective in removing the surface defects (i.e., good or ideal chemical passivation of defects). Nanometer-scale point contact openings with pitch of a few tens of nanometers give the best results for the structures we considered. We identified the fill factor as the main performance bottleneck and showed that lower series resistances (leading to higher fill factor), can be obtained with thin passivation layer and high doping density (≥10 17 cm −3 ) of buffer layer, but also removing the CdS from the top of the passivation.
Simulations of the CdS-buffered cell showed that positive charge in the order of 10 12 cm −2 within the passivation can improve the efficiency of a cell with ideal chemical passivation by about 3.4% absolute, mainly thanks to better fill-factor. This field-effect passivation is even more effective in the case of inefficient chemical passivation. The positive charge also helps relaxing the requirements on the point contact geometry: point contact widths up to 20 nm can be used without significant efficiency loss.
Front contact nanostructured CIGS-based solar cells with different buffer layers (Zn(O,S), ZnO, Zn 0.81 Mg 0.19 O, In 2 S 3 ) have also been simulated, demonstrating that when the positive charge within the passivation is sufficiently high (in the range 10 12 -5·10 12 cm −2 ), the benefit of field-effect passivation also applies to cells having unfavorable conduction-band offset (i.e., cliff or low spike) at the buffer/CIGS interface, yielding efficiencies over 21% for all samples, and allowing more flexibility in the choice of the buffer layer.
Finally, it is worth pointing out that the efficiency ceiling (21.6%) shown by the simulated cells of this work is determined by the choice of the baseline structure, and is not an intrinsic limitation of the passivation/point contact process: under favorable conditions of chemical and field-effect passivation, an optimized front nanostructure can recover the efficiency loss due to interface recombination, boosting the efficiency to the value which is obtained when the bulk properties are limiting the cell performance. Table 6 Cell parameters under AM1.5G illumination for the cell in Fig. 9, in the case of a GB in the middle of a contact opening. 2D simulations.