IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 1, JANUARY 2013

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Modeling the Effects of Na Incorporation on CIGS Solar Cells Elif Selin Mungan, Student Member, IEEE, Xufeng Wang, Student Member, IEEE, and Muhammad Ashraful Alam, Fellow, IEEE

Abstract—In this paper, we quantitatively evaluate the relative importance of three mechanisms that are proffered by various groups to interpret the effects of sodium (Na) incorporation in copper indium gallium diselenide solar cells. The suggested mechanisms are 1) increase in the carrier density due to defect passivation; 2) spatial redistribution of gallium (Ga); and 3) change in the crystal orientation. The simulation framework which is developed for this purpose indicates that, among these three coexisting effects, the increase in the carrier density with Na incorporation is likely to be most important. If the grain boundaries (GBs) initially contain donor-like traps that are subsequently passivated by Na, the increase in carrier density can improve the cell efficiency significantly. On the other hand, we find that the effects of Ga redistribution and change in crystal orientation are limited.

Fig. 1. Changes observed in CIGS material properties with Na incorporation: [A] Increased carrier density (via Na doping or passivation of the GBs), [B] Ga segregation, and [C] change in crystal orientation.

Index Terms—Grain boundaries (GBs), photovoltaic (PV) cells, semiconductor device modeling, thin-film devices.

I. INTRODUCTION OLYCRYSTALLINE copper indium gallium diselenide (CIGS) is a promising thin-film photovoltaic (PV) material because, unlike several other alternatives, its high efficiency does not appear to be degraded by the grain boundaries (GBs) [1]. There is also a broad consensus based on empirical observations that the sodium (Na), which originates from sodalime glass substrate and diffuses through Mo layer, as shown in Fig. 1, can increase the cell efficiency significantly [2]. Despite many hypotheses and related experiments, the mechanism that leads to this increase in efficiency is still not clearly understood. In the literature, both an increase and a decrease in the grain sizes have been reported for Na-incorporated CIGS absorber layers. In both cases, the efficiencies of the cells have improved [3], [4]. An increase in the cell efficiency despite the smaller grain size might indicate the GBs become more “benign” with Na incorporation. Alternatively, it is also possible that an improvement in the bulk material properties due to Na incorporation compensates for the performance degradation due to GBs for an overall improved efficiency. So far, it has been difficult to decouple these effects experimentally.

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Manuscript received June 2, 2012; revised August 1, 2012; accepted September 5, 2012. Date of publication October 18, 2012; date of current version December 19, 2012. This work was supported by the Semiconductor Research Corporation Energy Research Initiative Network for Photovoltaic Technology. The authors are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906 USA (e-mail: ebaytok@purdue. edu; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JPHOTOV.2012.2221082

In order to find the reason underlying the efficiency improvement, one can systematically review the experimentally observed changes in CIGS material properties with respect to Na content. As shown in Fig. 1, these changes can be classified into three broad categories. The first of these changes involves an increase in carrier density with Na incorporation. Although the reason underlying this increase is still being debated, the increase in carrier density has been experimentally observed by many groups [5], [6]. The second change is related to the decrease in the [Ga]/[In+Ga] ratio toward the center of CIGS absorber layer, which causes an unintentional bandgap gradient [4], [7] that can potentially affect charge collection. Finally, several groups have noted that Na affects the morphology of CIGS growth. Specifically, the number of 1 1 2 oriented grains appears to increase after Na is incorporated [3], [8]. Since various changes in physical properties attributed to Na incorporation occur simultaneously, it has been difficult to de-embed their relative contributions toward the efficiency of CIGS cells. Therefore, we develop a comprehensive numerical modeling framework to explicitly and simultaneously account for these three Na-related phenomena and quantitatively assess respective contribution of each mechanism. It is unlikely that a theoretical simulation, however sophisticated, will settle a long-standing debate such as the role of Na on CIGS efficiency. Our study, however, offers many insights that will help design of future characterization experiments to conclusively interpret the origin of efficiency gain in Na-rich CIGS cells. The rest of this paper is organized as follows. First, we explain the modeling framework in detail. This section is followed by a systematic numerical analysis of the three hypotheses discussed previously that might explain the improvement of the cell performance with Na incorporation. Finally, we conclude with a brief assessment of our findings.

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IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 1, JANUARY 2013

TABLE I PHYSICAL PARAMETERS USED IN THE MODEL

Fig. 2. (a) Single-crystalline and (b) polycrystalline CIGS structures used in the simulations. (c) SEM image of the CIGS sample on the Mo substrate. (Reprinted with permission from [1]).

II. SIMULATION FRAMEWORK Simulations are carried out in Sentaurus (a commercial 3-D device simulator [9]) for a 1-μm-wide CIGS cell with a 3-μm-thick absorber, a 50-nm-thick CdS buffer layer, and a 200-nm-thick ZnO window layer. The optical and physical parameters for various layers are taken from [10]. To investigate the effects of the GBs, multiple GBs are implemented within the device using an idealized Manhattan geometry, as in Fig. 2(b). Although we can simulate any arbitrary spatial distribution of GBs, for the illustrative example considered here, the GBs are placed in decreasing numbers toward the CdS/CIGS interface to mimic the real-life polycrystalline CIGS structures, as shown in Fig. 2(c) [1]. It should be noted that the performance of a solar cell depends on the specific distribution of GBs within the absorber material. A simpler structure with larger grain sizes will have longer carrier lifetimes, correspondingly higher fill factor (FF), open circuit voltage (VOC ), and efficiency (Eff). In the literature, the electrical properties of GBs are defined by various density and energy levels of traps [10]–[12]. Following [10], we will use four different types of traps to model the GBs. These are 1) neutral traps; 2) acceptor-like traps; 3) donorlike traps with no valence band discontinuity; and 4) neutral traps in a valence band-shifted region. The acceptor- and donorlike traps (“2” and “3”) are set to be neutral when unoccupied, while they are negatively and positively charged, respectively, when fully occupied [13]. While evaluating charged traps, two of their fundamental properties, namely, recombination velocity sR and trapped charge density, are treated as independent variables. We assume that the surface recombination velocity sR is dictated by midgap trap states with large capture cross sections. On the other hand, the charge density is dictated by the trap states that are closer to the respective band edge (e.g., conduction band for donor-like traps), with smaller capture cross sections. For the fourth type of trap, it is assumed that a neutral GB is surrounded by a 20-nm-wide region, in which the valence band is shifted down 0.2 eV in energy due to Cu depletion [14]. The physical parameters that are used to model the GB recombination are summarized in Table I. Here, the trap density of the charged traps NT is chosen to be 4.5 × 1011 cm−2 , since in [10] this density of traps leads to the minimum efficiency for a CIGS cell with a single vertical GB. For NT values that are higher than this value, an inversion occurs at the GB, which reduces the recombination at GB and improves the cell’s efficiency [10].

Fig. 3. Band diagrams and corresponding recombination rates for a GB model with (a) localized donor-like traps with no valence band discontinuity near the GB and (b) neutral traps in a valence band-shifted region.

The capture cross sections (σe , σh ) that are used to model the trapped charge density are assumed to be 10−18 cm−2 to ensure that these near band-edge traps contribute to charging, but not to carrier recombination (here, the recombination velocity is 0) so that the minority carriers are repelled from the interface, and SRH recombination is minimized. Finally, if the GBs in CIGS are modeled by neutral traps and the material in the vicinity of the GBs have a larger bandgap, it gives rise to the band diagram in Fig. 3(b). The valence band offset acts as a barrier for holes, while there is no barrier for electrons. This barrier has an effect on the cell efficiency similar to that of donor-like trap, embedded in a GB with no discontinuity in valence band. Once the valence

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Band diagram of the double-graded single-crystalline structure.

band shift ΔEV is significant enough (as in Fig. 4), the majority carriers are repelled from the neutral GB to the extent that they become the limiting factor for the recombination. Thus, the recombination rate at GBs reduces. For a Cu-depleted GB in CIGS, ΔEV can go up to 0.4 eV [14], which would suppress the recombination at GB significantly. The results in Fig. 4 suggest that, for example, for a device defined by sR of 105 cm/s, the efficiency can improve by ∼11% when the charges on the donor-like traps are reduced by Na incorporation and the traps become neutral. It should be noted that the trapped charges along GB and sR are not isolated variables. For instance, an annealing step might reduce the trap densities throughout the bandgap which would reduce the effects of both trapped charges and the sR of the GB. Thus, a larger improvement margin can be achieved. This improvement margin is also related to the number of trapped charges on donor-like traps in the GBs. In order to provide a rough idea about this relation, the efficiency values that correspond to a different NT (4 × 1011 cm−2 ) have been provided in Fig. 4. The results indicate that the efficiency recovers rapidly even with a modest reduction in NT (∼10%). It should be clear from the aforementioned analysis that had the GBs been defined by other types of defects (e.g., neutral, acceptor-like, etc), the effect of Na incorporation would have been far more modest. B. Hypothesis 2: Change in Ga Distribution Due to the reduced interdiffusion between Ga and In in the presence of Na, a decrease in the amount of Ga concentration around 500 nm away from the CdS/CIGS interface has been observed by several groups [4], [7]. To investigate the effect of this change in the composition on cell performance, double-graded single-crystalline and polycrystalline geometries [as in Fig. 2(a) and (b)] are generated. The NT value for donor-like traps was chosen to be 4 × 1011 cm−2 , for ease of comparison since the performance metrics for NT = 4.5 × 1011 cm−2 are very low for sR of 105 cm/s (see Fig. 4). Absorption coefficients and bandgap values with respect to the Ga mole fraction are taken from [18] and [19]. The change in the bandgap is only reflected through electron affinity, while the valence band position is presumed to remain the same. The [Ga]/[Ga+In] ratio is kept at 0.3 in the front and at 0.5 in the back of the CuIn(1−x) Gax Se absorber, as in [1], while the minimum bandgap occurs at ∼500 nm from the junction, as shown in Fig. 5. Afterward, the [Ga]/[Ga+In]

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IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 1, JANUARY 2013

Fig. 6. Performance metrics values with respect to the [Ga]/[Ga+In] ratio 500 nm from the heterojunction. The double-graded absorber is singlecrystalline , polycrystalline with neutral traps (−•−), and polycrystalline with donor-like traps with N T = 4 × 101 1 cm−2 (--).

Fig. 7. Performance metrics values with respect to the distance of the homojunction from the heterointerface and the doping density N D of the Cd diffused n-type layer. N D = 101 6 cm−3 , N D = 5 × 101 6 cm−3 (−•− ), and N D = 101 7 cm−3 (--).

ratio of this point is varied to explore its implication for cell efficiency. The results summarized in Fig. 6 indicate that, for the given range, the efficiency of the cell degrades with the reduction in Ga mole fraction (and therefore the bandgap) at ∼500 nm from the CdS/CIGS heterojunction. As the minimum bandgap decreases, so does the effective bandgap of the double-graded junction, leading to a reduced VOC . On the other hand, this decrease in the bandgap increases absorption and, therefore, JSC . However, the loss in VOC due to the decreased bandgap is larger than the gain in JSC , resulting in a net loss in overall efficiency. VOC is suppressed due to recombination at GBs for the polycrystalline cells in Fig. 6. Therefore, the decrease in the absolute efficiency values with respect to the composition gradient is found to be less prominent for polycrystalline structures. If the Ga mole fraction at minimum bandgap point is reduced from 0.3 to 0.2 (to be similar to [1]) due to Na incorporation, the efficiency of the cell would have been reduced by ∼1% for the singlecrystalline CIGS material. On the other hand, this reduction would be 0.58% for polycrystalline material with neutral traps and 0.71% for polycrystalline material with donor-like traps.

additional electric field that is introduced by the buried homojunction improves the carrier collection. This improvement is mainly visible in JSC and FF in Fig. 7. Thus, increasing doping depth and doping concentration do improve the efficiency. However, for a typical homojunction depth around 80 nm, as in [21], the increase in the efficiency is modest (