Grain boundaries in Cu(In, Ga)(Se, S) 2 thin-film solar cells

Transcription

1 Appl Phys A (2009) 96: DOI /s INVITED PAPER Grain boundaries in Cu(In, Ga)(Se, S) 2 thin-film solar cells Uwe Rau Kurt Taretto Susanne Siebentritt Received: 18 July 2008 / Accepted: 4 November 2008 / Published online: 3 December 2008 Springer-Verlag 2008 Abstract The paper reviews the current status of the research on grain boundaries in polycrystalline Cu(In, Ga) (S, Se) 2 alloys used as absorber materials for thin-film solar cells. We discuss the different concepts that are available to explain the relatively low electronic activity of grain boundaries in these materials. Numerical simulations that have been undergone so far to model the polycrystalline solar cells are briefly summarized. In addition, we give an overview on the experiments that have been conducted so far to elucidate the structural, defect-chemical, and electronic properties of grain boundaries in Cu(In, Ga)(S, Se) 2 thin-films. PACS Gr Pz Hk Jt 1 Introduction The semiconductor Cu(In, Ga)(Se, S) 2 (CIGSS) provides the absorber material for solar cells with the highest power conversion efficiency of all thin-film photovoltaic devices [1]. The grain size g of these polycrystalline films hardly exceeds the film thickness d of typically d = µm. Obviously, the electronic activity of grain boundaries (GBs) in such a situation is much more critical than it is in multicrystalline Si solar cells with g being of the order of g = 5 10 mm. Furthermore, solar cells made from polycrystalline CIGS absorbers with efficiencies above 19% [1 3] markedly outperform their 12.5% efficient monocrystalline counterparts. 1 Understanding the physics underlying the electronic activity of GBs in CIGSS is therefore not only important for improving the efficiency of CIGSS solar cells but also could provide general insight into the requirements for highefficiency polycrystalline solar cells. The present paper reviews the current status of the research on GBs in the chalcopyrite alloys for photovoltaic applications. Section 2 yields a short introduction into the electronic properties of GBs and their impact on the performance of polycrystalline solar cells and then discusses the different concepts that are available to explain the low electronic activity of GBs in CIGS. Section 3 reviews the numerical simulations that have been undergone so far to model polycrystalline CIGS solar cells. In Sect. 4 we give an overview on the experiments that have been conducted so far to elucidate the structural, defect-chemical, and electronic properties of GBs in CIGS. Section 5 summarizes simulations and experiments. U. Rau ( ) IEF5-Photovoltaik, Forschungszentrum Jülich, Jülich, Germany u.rau@fz-juelich.de K. Taretto Dto. de Electrotecnia, Universidad Nacional del Comahue, Buenos Aires 1400, Neuquén, Argentina S. Siebentritt Université du Luxembourg, 162a, avenue de la Faïencerie, 1511 Luxembourg, Luxembourg 2 Grain boundary models 2.1 General remarks on grain boundaries in solar cells The primary effect of a GB on a crystalline semiconductor material results from the interruption of the long-range 1 Active-area efficiency of a CuInSe 2 cell reported by [4]. We notice that this cell uses a simple, un-optimized front contact (strongly suffering from series resistance), and no antireflection coating.

2 222 U. Rau et al. either assume a distribution function D(E) that is continuous in energy [7] or a defect concentration N it at a fixed energy E it likeinref.[8]. In the latter case it is useful to consider that half of the defects are acceptors and the other half are donors such that for large concentration N it the Fermilevel is pinned at E it. With these assumptions, the charge density Q GB obeys Fig. 1 Calculated band diagram in a Cu(In, Ga)Se 2 semiconductor across two grain boundaries (GB) located at y = 0.5 and 1.5 µm. The diagram a corresponds to thermodynamic equilibrium at room temperature, while b is obtained at solar illumination under short-circuit conditions. The energies E V and E C are the energies of the valence and conduction band edge, respectively, and E it is the GB defect energy, here located at ev above the valence band edge. Additionally shown are the GB barrier height Φ b and the band-bending energy qv b. In part b, the hole and electron quasi-fermi levels E Fp and E Fn,are defined. The assumed GB trap density is N it = cm 2 order provided by the periodicity of the crystal. In general such interruption leads to electronic states at energies that are forbidden within the bulk of the crystal [5]. The states eventually result in an electronic charge Q GB (by unit area) at the GB that, in turn, is counterbalanced by a space charge region surrounding the GB [6]. Figure 1a displays the band diagram across two charged GBs in a p-type semiconductor calculated under thermal equilibrium conditions. The band bending V b at the GB is linked to the width w SC of the space charge region via V b = qn A wsc 2 2ε, (1) S where N A is the doping density, q the elementary charge, and ε S the absolute dielectric constant of the semiconductor. The charge resulting from the space charge regions at both sides of the GB is given by Q SC = 2qN A w SC and must equal Q GB. Therefore, we may rewrite (1)as V b = Q2 GB. (2) 8qN A ε S The charge Q GB, in turn, depends on the density N it of the electronic states at the GB and their occupation. There are different ways to model the density of GB states: One may Q GB = qn it 2 (1 2f it), (3) where f it is the occupation function of the assumed donor/ acceptor GB defects, given by the Fermi statistics depending on the position of defect energy E it relative to the Fermi energy E F. The barrier height shown in Fig. 1a corresponds to a defect density N it = cm 2 and a defect energy at E it E V = 0.88 ev, i.e., on the upper half of the 1.2 ev band gap. Figure 1a shows that in this situation, the equilibrium Fermi level E F at the GB is pinned to the energy of the trap, i.e., closer to the conduction band edge than to the valence band edge indicating that carrier-type inversion is occurring at the GB under these assumptions. Under solar cell operation, the photogenerated carriers will occupy GB defect levels, reducing the GB charge and the barrier height, as shown in Fig. 1b, where we also see that the Fermi level is split in the quasi-fermi levels E Fn and E Fp for electrons and holes. Additionally, the photogenerated carriers will suffer from recombination through GB defect levels, with the net recombination rate given by N it v th (n it p it n 2 i R it = ) σ 1 it,p (n it + n 1,it ) + σ 1 it,n (p it + p 1,it ), (4) where v th is the carrier thermal velocity, σ it,n and σ it,p the GB defect capture cross sections for electrons and holes, n it and p it are the local electron and hole concentrations at a given point of the GB, and ( ) Eit E C n 1,it = N C exp (5) kt and ( ) EV E it p 1,it = N V exp (6) kt are auxiliary quantities, E it being the energy of the considered trap level. 2.2 Cu(In, Ga)(Se, S) 2 basics The alloy system of the Cu-chalcopyrites Cu(In, Ga)(Se, S) 2 includes a wide range of band gap energies E g from 1.04 ev in CuInSe 2 up to 2.4 ev in CuGaS 2 [9]. These semiconductors belong to the I III VI 2 materials family that crystallizes

3 Grain boundaries in Cu(In, Ga)(Se, S) 2 thin-film solar cells 223 in the tetragonal chalcopyrite structure [10]. All these compounds have a direct band gap making them in principle suitable for thin-film photovoltaic absorber materials. Most efficient solar cells are made from the alloy Cu(In 1 x,ga x )Se 2 with a moderate Ga-content x with E g ev. This holds for the record laboratory devices [1 3] and for commercial products that currently enter into the mass market [11 14]. Many research efforts are made to use the full alloy system of Cu-chalcopyrites to produce solar cells, e.g., with a large band gap energy E g 1.5 ev (for reviews on wide-gap chalcopyrites see [15, 16]). The increase of E g by increasing the amount of Ga in Cu(In 1 x,ga x )Se 2 films leads to a decline of the electronic properties of the material starting approximately at x = 0.3 [17, 18] that up to now makes this wide-gap option not attractive for commercial production. The material Cu(In, Ga)S 2 yields a laboratory record efficiency η = 12.3% [19] with a small Ga content corresponding to a band gap energy E g 1.55 ev. This type of material is the base for the currently only commercial activity using wide-gap chalcopyrites [20]. We emphasize at this point that there exists a basic difference between the photovoltaic grade materials from the Cu(In 1 x,ga x )Se 2 class and those of the sulphide class. Cu(In 1 x,ga x )Se 2 films acting as absorbers for high-efficiency solar cells are generally made with a Cu-poor overall stoichiometry (denoted as Cupoor in the following), whereas Cu(In, Ga)S 2 is prepared under Cu-rich conditions. This preparation method leads to the segregation of CuS secondary phases [21 23] that are removed by KCN etching, leaving the nearly stoichiometric chalcopyrite, before the device can be processed further. Despite of these differences, the basic device structure for all chalcopyrite thin-film solar cells is as sketched in Fig. 2. The preparation of all CIGSS-based solar cells starts with the deposition of the absorber material on a Mo-coated glass substrate. For this step, several deposition methods are available, where the co-evaporation of all elements yields the absorber material with the highest efficiencies. There exist several variations of the co-evaporation process with different sub-steps or stages for the deposition [24, 25]. High efficiencies are also obtained from absorbers prepared by the selenization (or sulfurization in case of Cu(In, Ga)S 2 ) of previously deposited metal precursors in the presence of either elemental Se or S [20, 26, 27] orh 2 Se [28 30] (likewise H 2 S[31]). In the following, we denote these types of absorber preparation two-stage processes because precursor deposition and compound formation are two welldistinguished processing steps. Regardless of the different absorbers and their various preparation methods, the thin-film solar cells are finished by the chemical bath deposition of a CdS buffer layer (E g 2.4 ev) and by sputtering of a ZnO window layer (E g 3.4 ev). The research on the physics and chemistry of buffer layers for CIGSS solar cells including Cd-free buffer/window combinations has been reviewed recently by Hariskos et al. [32] and by Siebentritt [33]. The resulting equilibrium band diagram of the ZnO/CdS/CIGSS heterojunction solar cell is shown in Fig. 3 for the case of low-gap alloys, e.g., CuInSe 2. The two-dimensional band diagram on the left combines the band bending around a GB (assumed perpendicular to the heterojunction) with the cross sectional view across the ZnO/CdS/CIGSS heterointerface. The one-dimensional diagram to the right ignores the GBs but features a more detailed view across the heterointerface with the band-offsets between the different materials including an internal valence band offset E V between the bulk of the CIGSS absorber and a Cu-poor surface layer on top of this absorber that has a higher band gap energy than the bulk [34, 35]. The Cu-poor surface layer shows up only if the absorber is prepared Cu-poor [34] and has a thickness of nm [36]. The band offset prevents holes from arriving at the metallurgical absorber buffer interface and is therefore thought to minimize losses by recombination of holes with electrons at that interface [37, 38]. 2.3 Grain boundary models for Cu(In, Ga)(Se, S) 2 Fig. 2 Sketch of the layer structure of a CIGSS thin-film solar cell with a Mo back contact on a glass substrate, the polycrystalline absorber material, the CdS buffer, and the ZnO window layer It is evident that the wide variety of material composition and preparation methods for CIGSS absorbers leads to very different absorber morphologies and grain geometries. Crystallography: The number of electronic states at the boundary between two crystals is obviously much dependent on the relative crystallographic orientation of the two adjacent grains. In this respect, twin boundaries are special grain boundaries without strained or dangling bonds, only the second nearest neighbors of the atoms along the GB have the wrong ordering. Twin boundaries have been

4 224 U. Rau et al. Fig. 3 Two- and one-dimensional band diagrams of a ZnO/CdS/CIGSS thin-film solar cell. The two-dimensional diagram on the left combines the band bending around a GB (assumed perpendicular to the heterojunction) with the cross sectional view across the ZnO/CdS/CIGSS heterointerface. The one-dimensional diagram to the right shows the more detailed view across the heterointerface featuring the band-offsets between the different materials including an internal valence band offset E V between the bulk of the CIGSS absorber and a Cu-poor surface layer found to be the dominating type of GB in chalcopyrite thin films (see Sect. 4.4 below). Intrinsic passivation: Yan and co-workers [39, 40] suggest that GB defects in CIGSS are intrinsically passivated. In this work, electronic states of defect structures of GBs with dislocation cores were calculated, i.e., GBs with broken and strained bonds, unlike twin boundaries. It was found that by relaxing the defect structures no electronic defects in the band gap are formed. Thus, even GBs with a high density of structural defects are not expected to develop charged electronic defects. Extrinsic GB passivation: The extrinsic passivation of GB defects is one important option for obtaining a good photovoltaic absorber material in spite of an initially high electronic activity of GBs. In CIGSS, the beneficial effect of post-deposition air-annealing, an important scheme to improve the device performance from the early days up to the present, was explained by oxygenation of GBs. Within the defect chemical model of Cahen and Noufi [41], the major charge at the GBs are positively charged Se vacancies. Oxygen is thought to passivate these Se vacancies. Later, Kronik and co-workers explained the beneficial consequences of the presence of Na during absorber deposition or in post-deposition Na treatments follows from its catalytic effect on oxygenation [42, 43]. Band Structure: It has been suggested that one important ingredient for the high performance of polycrystalline CIGS thin-film solar cells stems from an internal valence band offset E V at the GBs (sometimes also referred to as a neutral barrier, as it provides a barrier to majority carrier transport even for a neutral grain boundary without defects) resulting from a slightly Cu-poor composition of the region adjacent to the GB [44, 45]. The starting point is the consideration that the stable surfaces in chalcopyrites are the polar (112) surfaces [46], which are stabilized by Cu vacancies and In Cu antisites, i.e., by becoming Cu poor [47, 48]. GBs in this model are considered Cupoor (112) planes. Because the valence band maximum in Cu(In, Ga)Se 2 is formed of Se-p and Cu-d states and is shifted up by the repulsion between them, removing Cu leads to a down shift of the valence band maximum. Thus the Cu-poor GBs along a (112) plane are expected to show a negative valence band offset compared to the grain interior [49 52]. The modeling of GBs along the (112) planes without Cu deficit did not result in a valence band offset [45]. The effect of this internal offset at the GBs could be of similar importance as it is at the surface of the absorber [37]. Whereas, there is ample experimental evidence for the Cu-poor surface layer [34, 35] and its beneficial consequences for the performance of CIGS solar cells as long as the overall film composition is Cupoor [36], the question whether or not such a Cu-poor layer is a general positive feature of GBs in CIGS is still under discussion. We will discuss this possibly important feature in some detail in Sect Numerical simulations A series of two-dimensional numerical device simulations for polycrystalline Cu(In 1 x,ga x )Se 2 has been performed

5 Grain boundaries in Cu(In, Ga)(Se, S) 2 thin-film solar cells 225 during the last few years [8, 53 56]. Although the two different groups having conducted these simulations use slightly different approaches, the basic results are very much consistent. The following summarizes mainly the most recent paper [8]. 3.1 Grain boundary barrier Figure 4 shows barrier heights Φ b obtained by numerical simulation, where bulk and GB defects with capture cross sections σ bt,n/p = σ it,n/p = cm 2 and defect energies E it = E V + 270, 605 and 880 mev were assumed. The defect densities cover two orders of magnitude from N it = to N it = cm 2. The considered doping density is N A = cm 3, and the bulk defect density is N bt = cm 3. Under equilibrium conditions (full symbols) and a low N it = , the barrier height Φ b equals the energy distance E F E C 160 mev in the bulk for all defect energies E it, reflecting that the energy barrier at the GB is negligible. Within the range N it = to cm 2, the barrier heights asymptotically approach the value of the corresponding defect energy (dashed lines in Fig. 4). For the interface defects close to the conduction band (E it E V = 880 mev), we find type inversion above N it cm 2. The band diagram shown in Fig. 1a corresponds to such a situation under equilibrium conditions. The reduction of band bending and that of the GB barrier Φ b by illumination is demonstrated more quantitatively by the open symbols in Fig. 4, especially for the trap energies E it E V = 880/605 mev, whereas the curve with E it E V = 270 mev is only little affected by illumination. This latter situation appears to be the most probable in current CIGS cells, since, assuming a Fermi energy 160 mev above valence band edge, E it E V = 270 mev would yield a barrier of qv b = 110 mev, in accordance with most experimental data discussed in Sect Computed solar cell efficiencies Here we investigate the influence of GB parameters on solar cell device performance. Figure 5a shows the solar cell efficiency η as a function of the GB defect density N it in a CIGS solar cell with identical, columnar grains with a size g = 2 µm. The bulk defect concentration is set to N bt = cm 3 and the capture cross sections to σ bt,n/p = cm 2, yielding a bulk minority carrier lifetime of τ b = 10 7 s and a diffusion length L D 5µm.The photovoltaic performance for N it = 0 yields a high reference efficiency of η 20%. The GB capture cross sections are equally set to σ it,n/p = cm 2, and the defect energies are assumed identical for bulk as well as GB with the values E bt = E it = E V + 270, 605, and 880 mev. Figure 5a shows that η decreases by increasing the number of GB defects, independently of the energy position of the traps, obeying an augmented recombination of carriers. Although Fig. 4 Grain boundary barrier heights Φ b with increasing GB defect density N it calculated in CIGS solar cells with a grain size g = 2 µm under illuminated, short-circuit conditions (open symbols), andinthedark(full symbols). Shallow defect levels (squares) located at E it E V = 270 mev above the valence band edge yield small barrier heights, which are only weakly increased by the addition of defect levels and are unaffected by illumination. Defects at E it E V = 605 mev (circles) ande t E V = 880 mev (triangles) build up significant GB barriers with increasing density N it. In the dark, the barriers saturate above N it = cm 2 due to Fermi level pinning. Solar illumination strongly reduce these barriers (open circles, open triangles). These results consider a doping density N A = cm 3 and a carrier lifetime-limiting bulk defect density of N bt = cm 3 Fig. 5 Calculated solar efficiency η for a Cu(In, Ga)Se 2 solar cell with grain size g = 2µma, for increasing GB defect density N it. The doping concentration is N A = cm 3, the bulk defect concentration is N bt = cm 3, and the capture cross sections to σ bt,n/p = cm 2. Bulk and GB defect levels use equal electron and hole capture cross sections σ bt,n/p = σ it,n/p = cm 2 and energy levels at 270/605/880 mev (squares, circles, stars) above the valence band edge. In part b, the results for a grain size g = 0.5 µm(full symbols) are compared to g = 2µm(open symbols, as extracted from part a) at a defect energy of 270 mev above valence band edge

6 226 U. Rau et al. this is the expected overall consequence of increasing N it,it is worth to notice that the defect energy plays an important role for moderate to high defect densities. Shallow traps (circles in Fig. 5a) are less harmful for GB recombination since they produce only small band bendings, yielding a relatively low GB recombination. Cells with GB traps above midgap (squares, stars) produce large band bendings and spacecharge regions, strengthening GB recombination. Compared to midgap defects, for E it = E V mev (stars), we notice that η falls at a slower pace above N it cm 2. Our simulations reveal that this concentration corresponds to the onset of type inversion at the GB under illumination, yielding the band diagram shown in Fig. 1b. Under these circumstances, the scarcity in holes limits recombination, despite the broad space-charge region around the GB. 3.3 Internal valence band offset Now we turn to the effect of the internal band offset E V along the GBs in order to establish the conditions that must be met if the Cu-poor layer should have a decisive beneficial effect on the performance of polycrystalline CIGS solar cells. Figure 6 represents an equilibrium band diagram across two GBs having an internal valence band offset. The offset effectively represents an energy barrier of width 2w and effective barrier height Φ b = Φ b + E V, where only the part Φ b results from the interface charges Q it.themostimportant implication for solar cell operation is that the barrier could prevent holes from reaching the GB, potentially reducing GB recombination. In device modeling, the reduced recombination probability is introduced by defining an effective hole capture cross section at the GB according to σ eff it,p = σ it,p exp( E V /kt), (7) which is introduced to modify the recombination rate in (3). Since the band offset is modeled through the capture cross Fig. 6 Equilibrium band diagram across two grain boundaries showing a band offset E V in the valence band edge around the GBs, effectively yielding an energy barrier of two times the width w and effective barrier height Φb. This barrier hinders holes from reaching the recombination active GBs, reducing grain boundary recombination sections, it is useful to define the capture cross section ratio r σ = σit,p eff /σ it,p, noting that it drops by one order of magnitude for an increment of the band offset E V by 60 mev at room temperature [8, 53]. In the following, we assume a high GB defect concentration (N it = cm 2 ) that serves as limiting case for maximum GB recombination activity, providing a physical picture of the impact of the internal band offset. Figure 7 displays the calculated conversion efficiency η foracellasa function of the ratio r σ, assuming σ it,n/p = cm 2.The value of r σ is reduced from 10 0 (no band offset E V = 0) to 10 6 ( E V = 360 mev). The results already show that with decreasing r σ, the device efficiency improves, independently of the defect energy, and high efficiencies above 19% require offsets of at least E V = 300 mev. When E it lies above midgap (full diamonds), the efficiency is overall higher than for midgap and shallow defects (circles, squares). This is explained realizing the operation of an additional physical effect, since at the high chosen N it = cm 2, the cell works under type inversion at the GB. Here, the population inversion effectively implies a reduced GB recombination and enhanced carrier collection through the GB, improving the cell s short-circuit current. Thus, an overall improvement of the solar cell efficiency by the internal valence band offset compared to the efficiency obtained with high GB trap density is expected from modeling point of view. This is found consistently for all available simulations [8, 53 56]. It should be pointed out though, that the achieved efficiency with a high band offset does not exceed the efficiency obtained without GB defects (see Fig. 5). A significant effect improving otherwise very recombination active GBs requires a value E V in the range of 200 mev, whereas for E V > 300 mev, recombination at GBs is virtually eclipsed. Such a value for E V is covered by the theoretical predictions [44, 45]. However, there are more requirements that have to be fulfilled: First, the Cu-deficient wide-gap region around the GB has to be a thickness of around 3 nm to prevent tunneling of holes from the bulk interior into defects at the GB. Second, the height of E V and the thickness of the Cu-poor region has to be homogeneous along the entire length of the GB. If the Cu-poor region extends only along a fraction of the GB length, the beneficial effect is virtually destroyed by recombination at the unprotected part of the GB [8]. Finally, it is important to note that as soon as the Cu-poor layer is thick enough, homogeneous enough, and has a large enough internal band offset to prevent holes to penetrate to the GB (and thereby reducing recombination), this barrier is more prohibitive for intergrain transport of holes. Thus, any GB that is not perpendicular to the collecting junction eventually blocks hole transport to the back contact and creates electronically dead volumes in the absorber film. A valence band offset of around 250 mev appears here as a critical value [8], that is not incidentally that value where the reduction of recombination

7 Grain boundaries in Cu(In, Ga)(Se, S) 2 thin-film solar cells 227 in Fig. 7 would become very appealing. Thus, the internal valence band offset is very unlikely the exclusive reason for the low GB activity in CIGSS thin films. 4 Experimental results 4.1 Grain boundary barriers: transport measurements As we have discussed above, the band bending V b along GBs and the corresponding barrier Φ b is a primary indication of the electronic activity of GBs. However, quantitative experimental access to these quantities in fine-grained polycrystalline materials is difficult. Temperature-dependent measurement of the film conductivity and the determination of the corresponding activation energy E a can give a Fig. 7 Simulated efficiency η as a function of the ratio r σ between effective and nominal hole capture cross sections at the GB, for defect energies E it = E bt = E t = 270 mev (circles)/605 mev (squares)/ 880 mev (full diamonds). The defect density at the grain boundary is cm 2, the grain size g = 2 µm, and the bulk defect density N bt = cm 3 with capture cross sections σ bt,n/p = cm 2 first hint to GB barriers. The activation energy in this case is the sum of the activation energies of the charge carrier concentration and of the mobility. Assuming that the activation energy is more determined by the temperature dependence of the mobility, it can be used as an upper limit of barrier height. However, as majority carriers have to overcome thousands of GBs if such a measurement is performed in a co-planar contact configuration with a contact distance of several millimeters, the thermal activation energy E a monitors the lower limit of these barriers. In addition, it is by no means certain that in every case E a corresponds to the band bending V b since the thermally activated conductivity of the grain interior may dominate the film conductivity. However, the general trend of these conductivity measurements, as given in Table 1, together with the activation energies of mobilities from Hall measurements, shows that in all investigated films [57 60] the activation energy is generally below 300 mev. Moreover, values in excess of 100 mev are only found in Na-free films. Especially the experiments that compare the same samples before and after air-annealing [57] or compare samples with and without Na-incorporation but otherwise prepared identically [59, 60] are helpful in understanding the role of oxygen and sodium. The hypothesis that air-annealing reduces the GB barrier height by passivating GB states is strongly supported not only by the conductivity measurements [57] but also by the analysis of completed solar cells before and after air-annealing [61, 62]. For what concerns the role of Na, the picture is more complicated as Na plays a substantial role already during film formation [63]. However, there is no simple trend that relates the grain size with the presence or absence of Na [64]. The influence of Na on the texture, i.e., the prefer- Table 1 Activation energies for the majority carrier transport in various Cu(In, Ga)(Se, S) 2 thin films derived from temperature-dependent conductivity [σ(t)]orhall measurements. The films have a thickness of 1 3 µm and are prepared either by co-evaporation of the elements or by a two-stage process. Line 8 describes a single twin grain boundary of CuGaSe 2 grown by metal organic vapor phase epitaxy on a GaAs wafer a Thesamplewith E a = 120 mev had a Cu-content of only 18 at% Ref. Material Preparation Analysis E a [mev] Remark method method 1 [57] CuInSe 2 Co-evap. σ(t) 250 (Na-free) initial 170 air-annealed 2 [58] Cu(In 1 x,ga x )Se 2 Co-evap. σ(t) 100 x = 0 (x = ) 30 x = [59] Cu(In 1 x,ga x )Se 2 Two-stage σ(t) 40 Na-cont. 350 Na-free 4 [60] Cu(In 1 x,ga x )Se 2 Co-evap. σ(t) Na-cont. a (x = 0.2) 250 Na-free 5 [69] CuInS 2 Co-evap. Hall 90 n-type p-type 6 [70] CuGaSe 2 Co-evap. Hall Cu-rich 7 [72] CuGaSe 2 Co-evap. Hall <20 mev Cu-rich 8 [73] CuGaSe 2 Single Epi-GB Hall 32 Cu-rich 9 [74] Cu(In 1 x,ga x )Se 2 Two-stage Hall 50 Na-cont.

8 228 U. Rau et al. ential orientation of the grains, is also a fact that additionally depends on other parameters like the Se supply duringgrowth[65, 66]. In addition to the role of Na during growth, there is evidence for the improvement of Na-free grown films by a post deposition incorporation of Na at relatively low temperatures [67]. This observation is best compatible with the passivation of GBs directly by Na or indirectly by its catalytic effect on oxygenation [42]. Combining conductivity with Hall measurements allows one to discriminate between the mobility and the charge carrier density contribution to the overall film conductivity. In a polycrystalline material it is reasonable to ascribe the measured Hall carrier density p H to the bulk of the grains and the Hall mobility µ H to the GB barrier height [68]. Temperaturedependent Hall measurements using p-type and n-type polycrystalline CuInS 2 films have been carried out as early as 1975 [69]. The activation energies of µ H for the best films turned out to be about 80 mev for the best n-type and mev and for p-type material. For polycrystalline CuGaSe 2 films with varying doping density and Cu-rich initial composition, activation energies of µ H between 60 and 135 mev were found [70, 71]. These results agree well with the observations by Kelvin probe force microscopy which allows the direct observation of potential barriers as discussed in the next subsection. It should be noted that other Hall measurements of polycrystalline CuGaSe 2 grown under Cu excess have shown no or very small barriers below 20 mev in the temperature dependence of the mobility [72]. Based on the available data, it is not possible to pin down the difference between the samples that show a barrier in the mobility and those that do not. Also shown in Table 1 is the activation energy of a single twin grain boundary of CuGaSe 2 grown epitaxially by metal organic vapor phase epitaxy (MOVPE) on a GaAs wafer [73]. Unfortunately, there is only one Hall experiment available that deals with Cu-poor Cu(In 1 x,ga x )Se 2 with low x, i.e., the material with the highest technological relevance. This experiment [74] determines an activation energy E a = 50 mev for µ H (in the temperature range 250 K T 300 K) of a Cu(In 1 x,ga x )Se 2 sample prepared by a twostage process. This result fits reasonably well to E a from conductivity measurements of similar films given in line 3 of Table Grain boundary barriers determined by scanning techniques Another access to the electrostatic barrier induced by GB charges is given by Kelvin probe force microscopy (KPFM) and other scanning techniques (for overviews on the methods, see, e.g., Refs. [75, 76]). The advantage of KPFM is that the method can be applied to relevant thin-film samples that are grown in the same way as the absorber films. Fig. 8 Kelvin probe force microscopy (KPFM) measurements on CIGS film with random orientation (from Ref. [82]). The twodimensional mappings show the topography z a and the measured contact potential (CP) b. The line scans display c the measured height z of the sample surfaces and the work function Φ (solid line) as determined from the CP along the lines printed in the maps KPFM measures the height variations on the sample surface and, simultaneously, employs the electrostatic forces between sample and tip that yield the contact potential and, finally, the work function of the specific point at the surface [77]. As shown exemplarily in Fig. 8, grains and GBs can be easily identified from both, the surface topography image and the KPFM image, recorded simultaneously. Evaluation of individual line scans unveils a characteristic dip of the work function across the GB (Fig. 8c). The dip results from the charges at the GBs and approximately corresponds to the built-in potential [78]. It has been argued that the ob-

9 Grain boundaries in Cu(In, Ga)(Se, S) 2 thin-film solar cells 229 Table 2 Grain boundary barrier heights determined from Kelvin Ref. Material Preparation Analysis E a [mev] Remark probe force microscopy (KPFM) and by transport method method measurements using a scanning 1 [80] CIGS (x = 0.2) Co-evap. KPFM 150 a tunneling microscope (STM) 2 [81] CIGS (x = 0..1) Co-evap. KPFM 130 a x = 0 0 x = 1 3 [82] CIGS (x 0.2) Co-evap. KPFM 300 random text. 0 (220)-text [83] CIGS Co-evap. KPFM a (220)-text., with Na a It should be noted that in this 0 (220)-text., no Na publication the surface potential is plotted which has the opposite 4 [84] CIS Co-evap. STM 100 sign of the work function, CIGS (x 0.2) discussed in the other publications 5 [77] CuGaSe 2 Co-evap. KPFM 100 mev served band bending results from the air exposure of the film prior to KPFM measurements. But the same band bending has been found in films never exposed to air [79]. Table 2 lists the results for the band bendings that have been found so far with KPFM for Cu(In, Ga)Se 2 [80 83] and CuGaSe 2 [77]. Upon scanning the Ga-content in Cu(In 1 x,ga x )Se 2 films from x = 0 to 1, Jiang and co-workers [81] found that the band bending was around 150 mev for Ga-contents between x = 0 and 0.3, whereas from x = 0.4 to 1 the band bendings were close to zero. However, the conclusion in Ref. [81] that the present problem in preparing high-efficiency Cu(In 1 x,ga x )Se 2 solar cells with x>0.4 is explained by the absence of the band bending is hard to accept in view of all results from the numerical simulations discussed above. In addition, the basic problem of the wide-gap chalcopyrites is not primarily their insufficient carrier collection that under certain circumstances could be counterbalanced by collection along the GBs. In contrast, the predominant problem is the open circuit voltage that is lower than it should be for an efficient wide-gap material [15, 16]. For the open circuit voltage, however, the absence of a band bending around the GBs would be anything but a bad sign. A correlation of the band bendings with the film texture has been found in Ref. [82], showing that in randomly textured films there is a band bending of about 300 mev, whereas no or even a slightly negative band bending was found in (220)-textured films. This result could be correlated to cathodoluminescence analysis of similarly prepared films, as will be discussed in the next section. The comparison of (220)-textured films with and without Na in Ref. [83] yields band bendings around 180 mev with Na and zero without Na. This result is opposed to all findings from the transport measurements in Na-free samples discussed above (Table 1), where consistently higher barriers (supposedly GB barriers) were found for Na-free samples when compared to Na-containing ones. However, none of these transport measurements were performed using (220)- textured films. The band bending for the Na-containing sample in Ref. [83] is nevertheless also in contrast to the zero or slightly negative band bending reported in Ref. [82]. A series of other scanning techniques were also used to characterize GBs in CIGSS. Local transport measurements by a scanning tunneling microscope unveiled a band bending of around 100 mev in CuInSe 2 and in Cu(In, Ga)Se 2 [84]. Scanning tunneling luminescence investigation of GBs in pure CuInSe 2 films indicate the presence of a hole barrier at the GBs [85]. By electroluminescence mapping of a pure CuGaSe 2 film, also a barrier to current transport at the GBs was found [86]. The grain boundary barrier has also been investigated by electro-assisted STM, where an electron beam in the electron microscope is used to manipulate the tunneling current of the STM measured in the same or the neighboring grain. A barrier to electrons, i.e., for minority carrier transport, has been found in CuGaSe 2 but not in CuInSe 2 [87]. This is the only report on an electron barrier in the literature. An EBIC (electronbeam-induced current) investigation determined considerably lower recombination velocities for twin boundaries in Cu(In, Ga)Se 2 than in GBs with other orientations [88]. Figure 9 summarizes the barrier heights obtained for Cu(In 1 x,ga x )Se 2 films by simple transport and by Hall measurements (see Table 1) and by the scanning techniques (Table 2). Except for four data points (three stemming from Na-free samples and one from a film with random texture), all measured potential barriers are below 200 mev. Potential barriers larger than 200 mev appear to be restricted to poor photovoltaic materials. The trend that the GB barrier drops from around 130 mev at low Ga-content x to close to zero for x>0.4, as observed in Ref. [81], is not in conflict with the data from other sources, except for the barrier heights around 100 mev for pure CuGaSe 2. Note however, that with similar samples often barriers as low as 20 mev have been measured [72].

10 230 U. Rau et al. Fig. 9 Dependence of measured barrier heights for CuIn x Ga 1 x Se 2 films on the Ga-content x obtained from simple transport measurements (open symbols, according to Refs. [57 60]), Hall measurements (half symbols [70, 72 74]) and from the scanning techniques KPFM [77, 80 83]andSTM[84](full symbols). The crosses identify Na-free samples 4.3 Cathodoluminescence Up to now we have only discussed the electrostatic consequences of GBs in CIGSS. However the most important factor for photovoltaic devices is the recombination of photogenerated charge carriers. The recombination activity of any given spot in an absorber can be investigated by cathodoluminescence (CL), preferably in combination with transmission electron microscopy at the same spot [82, 89, 90]. In a recent detailed study the results of KPFM and of cathodoluminescence (CL) in the transmission electron microscope were correlated for device grade absorbers with different film textures [82]. The CL part of this study is summarized in Fig. 10, where CL images (top) and bright-field transmission electron micrographs (bottom) are shown for CIGS films grown without (a) and with Na-barrier layer on soda-lime glass. Both films have a (220) texture, but the sample with Na exhibits an almost homogenous CL/TEM mapping, whereas the Na-free sample has not only smaller grains but also a sharp CL contrast at the GBs. This result agrees with most investigations on the effect of Na in CIGS in so far that the photovoltaic performance of Na-free samples is poor, especially what concerns the open circuit voltage as a measure for the overall recombination activity in thefilms.thesamestudy[82] has also unveiled that the recombination activity of GBs in (112)-textured films is larger than in (220)-textured films. This finding is in agreement with KPFM investigations on similar films showing no band Fig. 10 Panchromatic cathodoluminescence (CL, top) mappings and bright-field transmission electron microscope (TEM, bottom) images (taken pairwise at the same places) of CIGS films grown on soda lime glass without a and with Na-barrier layer. Both films have a (220) texture [82].The sample with Na a exhibits an almost homogenous CL/TEM mapping, whereas the Na-free sample has not only smaller grains but also a sharp CL contrast at the GBs bending around GBs in (220)-textured films indicating that GBs with a band bending do indeed increase the recombination at the GBs compared to the bulk, while those without band bending show no increase in the recombination level. From another cathodoluminescence study on CuInS 2 it was concluded that twin boundaries show a much lower recombination activity than other GBs [91]. Reduction of cathodoluminescence intensity, together with a spectral shift, has also been observed [90] in absorbers with (112) texture used in high-efficiency Cu(In, Ga) Se 2 solar cells [3]. Unfortunately no equivalent investigations are available for the latest record solar cells where the absorbers show (220) texture [1, 92]. 4.4 Crystallography of grain boundaries A main conclusion from the experimental observation described in the previous paragraph is the existence of different types of GBs, which can at least partly be related to the texture of the films, as exemplarily discussed for the case of polycrystalline silicon in Refs. [93 95]. It can be expected that the main effect of different film textures is a difference in the crystallography of the GBs. Although it

11 Grain boundaries in Cu(In, Ga)(Se, S) 2 thin-film solar cells 231 cannot describe all details of the grain boundary structure, an important concept for the categorization of GB structures is the coincidence site lattice (see, e.g., [96]). This method describes the relative orientation of the two point lattices: by virtually extending the point lattice of one crystal into the other crystal certain lattice points of the two crystals coincide. The lattice of these coincidence points is the coincidence lattice which has a unit cell which is n times larger than the unit cell of the original lattice. This is the value of the grain boundary. The formation energies of grain boundaries depend on the value. Particularly low formation energies are found for the lowest value possible, the 3. 3 grain boundaries are just twin grain boundaries. From a simple model assuming complete orientation of the grains and vertical grain boundaries it has been suggested that (220)-textured films would contain 3 grain boundaries, while (112)-textured films would contain no 3 grain boundaries [73]. However, GBs in theses polycrystalline films generally are not vertical. In fact it was shown that vertical grain boundaries occur in Cu(In, Ga)Se 2 only under very special growth conditions [97]. A detailed electron back scatter diffraction (EBSD) analysis covering CuInSe 2, CuGaSe 2, Cu(In, Ga)Se 2, and CuInSe 2 films by Abou-Ras et al. has shown that by far most GBs in all these chalcopyrite polycrystalline films are in fact (near) 3grain boundaries, independent of the texture or the composition of the film [98]. The occurrence of twinning can be explained by investigating the local structure of the neighboring grains [97, 99]. These grain boundaries were shown to be along (112) planes. A similar result has also been obtained by a TEM study of structural defects in a polycrystalline CuInSe 2 film [100]. 4.5 Internal valence band offset Grain boundaries along (112) planes have been predicted to show a valence band offset when they are Cu-poor [44, 45]. A valence band offset of 550 mev has been predicted for CuGaSe 2. In an effort to measure the valence band offset at a single grain boundary, a twin grain boundary was grown epitaxially using a twin grain boundary in a GaAs substrate as a template [101]. With this single grain boundary with macroscopic grains on either side, it was possible to analyze the electronic structure of this twin grain boundary [73]. KPFM measurements show neither dip or bump in the work function scan across the grain boundary, indicating that the grain boundary has no charged defects, as can be expected for a twin boundary. Hall measurements across the boundary, on the other hand, showed an activated behavior of the mobility across the grain boundary, demonstrating that there is a barrier to majority carrier transport, albeit small. A neutral barrier of mev due to an internal valence band offset was found. These measurements were performed at epitaxial grain boundaries grown under Cu excess. It was not possible to grow epitaxial grain boundaries under Cu deficit. Although various amounts of Cu excess have been investigated and no trend in the barrier height with Cu content was found [102], it can not be excluded that grain boundaries grown under Cu deficit might actually show a higher barrier, since the barrier is associated with the Cu deficit of the grain boundary. However a neutral barrier of this height will hardly influence the efficiency of solar cells at room temperature. 4.6 Grain boundary composition A major difference between the various grain boundary models discussed in Sect. 2.3 above is the composition of the grain boundary. While the extrinsic passivation relies on the presence of oxygen and sodium at the grain boundary, the neutral barrier model requires a Cu deficient grain boundary. The available experimental results do not allow clear conclusions on the composition of grain boundaries. High spatial resolution micro Auger measurements have found a Cu deficit at grain boundaries [50], whereas neither Z- contrast measurements nor energy dispersive X-ray emission (EDX) measurements in the transmission electron microscope could detect a decrease in Cu content at the grain boundaries [51, 52]. The same is true for impurities at grain boundaries: a micro Auger study has found an increase of oxygen and sodium at the GBs [103], while the EDX study has not [51]. A recent investigation [91] of the phase contrast in the transmission electron microscope has indicated very large inner potential wells above 1 V over distances of a view nm, which can only be attributed to compositional changes at the grain boundaries. However, much smaller potential wells of 185 mev were found at twin boundaries. 5 Discussion and conclusion In view of the large variety of preparation methods and the wide range of alloy compositions used in research and development for Cu-chalcopyrite based solar cells, there are astonishingly few experimental data available that give information on the physical properties of GBs in these films. This lack of experimental data already indicates that GBs in CIGSS do not cause exorbitant problems for this type of solar cells because, otherwise, more research would have been directed towards this topic from the beginning. Thus, GBs in CIGSS cannot have an immoderate electronic activity. This follows also from the high solar cell efficiencies that have been achieved on the cell and on the module level with this relatively fine grained material. On the other hand, a further increase of device performance and a large-scale production

12 232 U. Rau et al. of solar modules on a high-efficiency level requires a detailed understanding also of minor loss mechanisms such as recombination at comparatively benign GBs. Eventually, the experimental results indicate differences between differently prepared materials, and the numerical simulations demonstrate the possible impact of these differences on the device performance. This is why we should carefully look at the available data and, after all, should conduct far more experiments dedicated towards a better understanding of GBs in CIGSS. To begin with, all experimental data indicate a low electronic activity of GBs in all investigated materials. The bulk of the measurements of the barrier height indicate a builtin voltage V b essentially below 200 mv. The values obtained from the most properly prepared films (e.g., prepared with Na) in each of the investigations yields even values V b 150 mv. This finding indicates a low overall concentration of charged GB defects and/or a charge neutrality position close to the valence band. Though this information is restricted to the electrostatic properties of GBs and tells nothing about their recombination activity, it is already a good message that few charges at the GBs do not attract minority carriers too much. During recent years, the high performance of fine-grained CIGSS solar cells in spite of the many GBs present has turned the discussion on GBs in these materials somewhat up-side down. Could we imagine that CIGGS is such a good photovoltaic material not despite of the many GBs but because of the GBs? One major argument for such a view is that the space charge region of the GB can be looked at as an extension of the space charge region of the heterojunction. Thus, minority carriers are attracted by the GB and guided via this channel towards the junction. Unfortunately, numerical simulations consistently could not unveil such a beneficial effect. In general, it was found that the band bending around a GB confines the short-circuit current density j SC towards the GB [8, 54], a situation that was also found in experiments [84]. However, this does by no means imply that the average j SC is increased by the GB. In most situations, the recombination losses that occur if the minority carriers travel along the GB lead to an overall decrease of j SC. Even under circumstances that lead to an enhancement of j SC, this advantage is outbalanced by the losses of V OC that are caused by recombination at GB defects. Metzger and Gloeckler found a specific situation (with mobilities μ e = 4cm 2 /V s and μ h = 1cm 2 /V s for electrons and holes) where the overall efficiency was enhanced by GBs. However, the efficiency level in this low-mobility case was only η = 15%. According to our preliminary conclusion, the electronic activity of GBs in CIGSS is controlled almost equally by crystallography and defect chemistry. Most GBs in properly grown films are low-energy GBs, most are even twin boundaries [98]. Possibly, even GBs with a less favorable crystallography leading to a high concentration of structural defects may not have an equal amount of electronically active defects [40]. Thus, GBs in CIGSS seem to be not very recombination active from the very beginning what provides already a good base for a reasonable photovoltaic device. On top of that, the beneficial effect of O and Na appears to result at least partly from GB passivation, as has been made plausible by several controlled experiments. This additional GB passivation, possibly together with the generally positive trend that may result from Cu-poor regions around GBs, eventually leads to the low GB activity that is imperative for making an outstanding record devices out of a reasonable one. 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