Performance predictions for monolithic, thin-film CdTe/Ge tandem solar cells

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1 Performance predictions for monolithic, thin-film CdTe/Ge tandem solar cells D.L. Pulfrey*, J. Dell, and L. Faraone School of Electrical, Electronic and Computer Engineering, M018 University of Western Australia, 35 Stirling Highway, Crawley, WA 6009 *Contact person (on leave from UBC, Vancouver, BC V6T1Z4): ABSTRACT Cadmium telluride thin-film solar cells are now commercially available and are being widely deployed in terrestrial, photovoltaic, power plants. However, the price of electricity from such sources would be more competitive with conventionally generated electricity if the cell efficiency could be improved without compromising the generally lowcost nature of the fabrication process. Recognizing that laboratory cells appear to have reached an efficiency limit of about 16.5%, we propose to improve on this by adding a thin-film germanium cell in a monolithic, tandem arrangement. Here we report on simulations of the photovoltaic performance of this structure, and we indicate that an efficiency improvement in excess of 20% may be attainable. 1. INTRODUCTION Thin film solar cells based on polycrystalline CdTe have been investigated extensively 1-3. While the technologies for deposition and recrystallisation of CdTe, and the formation of the CdS/CdTe junction are well developed, there still appears to be some controversy over why these devices perform so well 4,5. Nevertheless, the high yields, reliability, and moderate efficiencies of the cells that have been developed to date has led to CdTe-based thin-film solar cells gaining an increasing proportion of the commercial solar cell market 6. In spite of the significant investments in the development of CdTe thin-film cells, their efficiency has not improved beyond the value of 16.5% reported in Attempts to improve the efficiency have generally taken the paths of: changing the material (for example using wider bandgap, ternary II-VI materials, such as CdZnTe 7 or CdMgTe 8 ); using graded bandgap structures 4 ; utilizing tandem cells based on combinations of II-VI materials (for example CdTe and CdHgTe 9 ). None of these approaches has yet to realize a robust, reproducible improvement in II-VI materials-based thin-film solar cells. Here, we investigate another option: a tandem-cell structure using germanium for the low-bandgap complement to the CdTe cell. Germanium is attractive for several reasons: it is a well-characterized material; it is an elemental semiconductor and, therefore, it does not have the control- and reproducibility-problems often associated with compound semiconductors; its deposition and recrystallization over a wide range of temperatures has been demonstrated 10, lending credence to the viability of a CdTe/Ge/low-cost-substrate structure. While the bandgaps of CdTe (~1.5 ev) and Ge (~0.67 ev) are not optimal for a two-component tandem cell 11, they are well separated and, as we show here, a Ge cell has the required capability of generating a photocurrent to match that of the best CdTe cells. We emphasize that the tandem-cell structure proposed here is of the thin-film variety, and should be realizable using deposition techniques that are, in principle, much simpler and lower cost than are used in the fabrication of tandem cells involving ternary and quaternary single-crystal semiconductors. In this paper, we assume that a thin-film Ge solar cell can be adjoined to a high-performance CdTe cell, and we focus on establishing the properties that the germanium material, and the junction between the CdTe and Ge, must have in order for the proven efficiency of stand-alone CdTe cells to be enhanced significantly.

2 2. MODELING The general form of the tandem-cell structure is shown in Fig. 1. The photocurrents of each cell under AM1.5G illumination were determined using the standard equations for absorption in the depletion regions and field-free emitter and absorber regions 12. For the CdTe cell, which we modeled for convenience as a homojunction, the front surface reflectivity, regional thicknesses, minority carrier diffusion lengths, and surface recombination velocities were chosen to give the same photocurrent density under AM1.5G illumination as measured for the record cell 3. The dark current for the CdTe cell was evaluated using this photocurrent and the measured open-circuit voltage of the record cell. In this manner, the CdTe homojunction cell mimics the record heterojunction cell, allowing us to concentrate on the properties that the Ge cell must have in order to produce a significant improvement in the overall efficiency. Figure 1: Tandem-cell structure modeled in this work. The photovoltaic performance of the CdTe cell is listed in Table 1. The slightly higher efficiency of our cell is due to an overestimation of the fill-factor, most probably resulting from our present neglect of parasitic resistances. The properties of the CdTe cell are listed in Table 2, along with properties of the Ge cell, which are discussed in the next section. These properties are based on those quoted elsewhere for polycrystalline, thin-film solar-cell material: CdTe 13 and Ge 14. The Ge-diode dark current was calculated from the standard equations for diffusion of minority carriers in short, field-free Table 1: Photovoltaic performance parameters for the record cell of Wu 3 and the CdTe cell used in our simulations. J sc (ma/cm 2 ) V oc (mv) FF PV efficiency (%) Wu Our model Table 2: Regional parameters for each cell: front-surface reflectivity, surface recombination velocities, doping densities, regional widths, minority carrier diffusion lengths. Reflectivity (%) S F, S B (cm/s) N d, N a (cm -3 ) x emitter, x absorber (micron) L e, L h (micron) CdTe 6.5 5x10 4, 1x10 7 1x10 18, 1x , , 0.23 Ge 0 1x10 3, 1x10 3 1x10 19, 2x , , 1

3 regions 15. The success of a tandem cell depends not only on matching the photocurrents, but also on the ability of the interface between the two cells to allow continuity of the photocurrent. This is usually achieved by creating a tunnel junction at the interface. In such a junction, the holes constituting the photogenerated current in the top cell recombine, via band-to-band tunneling, with photogenerated electrons from the bottom cell. Such a junction is made from degenerately doped regions, and can be conveniently modeled by simulators that have a non-local tunneling capability 16. We used Sentaurus from Synopsys for this purpose. The equilibrium band-diagrams for the tunnel junction and the entire solar cell are shown in Figure 2. The n + emitter of the Ge cell forms one side of the tunnel junction, and a 100-nm, p + CdTe region was introduced to make the other side. Both sides of the junction were doped at a density of 2x10 19 cm -3. The band alignments at the interface were computed from: the bandgaps, an electron affinity of 4.0 ev for Ge, and a valence-band offset between CdTe and Ge of ev 17. Figure 2: Energy band diagrams. Left: the complete cell. Right: enlargement of the tunnel-junction region. 3. RESULTS AND DISCUSSION The Ge properties listed in Table 2 led to a Ge solar cell with a photocurrent density of 25.8 ma/cm 2, i.e., essentially identical to that of the CdTe cell (see Table 1). This excellent match can be inferred from the complementarity of the spectral responses of the two cells, as shown in Fig. 3. As the photocurrents are so well matched, the efficiency of the tandem cell is the sum of the values of the two individual cells. As Table 3 shows, this leads to a total efficiency of Table 3: Predicted photovoltaic performance of the Ge cell and the CdTe/Ge tandem cell. J sc (ma/cm 2 ) V oc (mv) FF PV efficiency (%) Ge alone CdTe/Ge tandem %, i.e., to an improvement of 28% over that of the stand-alone CdTe cell listed in Table 1.

4 Figure 3: Spectral photocurrents for the CdTe and Ge cells under AM1.5G illumination. The absorption coefficients used to obtain this figure were calculated from optical constant data listed in Palik 18. The photocurrent-matching of the Ge cell to the CdTe cell is not very sensitive to conditions in the emitter of the Ge cell because the emitter is only 100-nm thick. For example, making the front surface more ohmic for minority carriers still allows an overall efficiency improvement of >20% to be obtained (see first two rows of Table 4). However, as the last 3 rows of Table 4 indicate, a less blocking back contact leads to rapidly deteriorating performance. In fact, for an ohmic contact, even with an unrealistically high value of minority-carrier diffusion length, the presence of the Ge cell actually reduces the overall cell efficiency. On the other hand, if both back- and front-contacts can be made reasonably blocking, then, as row 3 of Table 4 suggests, an electron diffusion length of 5μm would be tolerable. However, attainment of such a value in polycrystalline material grown on a low-cost substrate will be challenging. The desired blocking nature of the back contact should be attainable by implementing a standard, low-high, isotype junction, but Table 4: Effect of minority carrier properties in the Ge cell on the overall improvement in efficiency of the tandem cell. S F (cm/s) S B (cm/s) L e (micron) V oc (mv) J sc (ma/cm 2 ) Ge PV efficiency (%) Efficiency improvement (%) 1x10 3 1x x10 7 1x x10 3 1x x10 7 1x x10 7 1x x10 7 1x keeping holes that are photogenerated in the n + -Ge away from the heterointerface may be more problematical because of the adverse curvature of the bands in this region (see Fig. 2). Assuming that these challenges can be overcome, the requirement remains for an effective tunnel junction. It is desirable that both materials forming the junction have low effective densities of states. This is so that the needed degree of degeneracy can be achieved at reasonable values of doping density. Unfortunately, the relevant effective densities of states for Ge (conduction band) and CdTe (valence band) are around 1x10 19 cm -3. For example, N V (CdTe) = 9.4x10 18

5 cm -3, based on heavy- and light-hole masses of 0.485m 0 and 0.117m 0, respectively 19. While extremely high p-type doping of CdTe (hole concentration of 5x10 19 cm -3 ) has been demonstrated using ion implantation and pulsed electron beam annealing 20, a lower cost technique would be needed for economical solar-cell production. Another desirable attribute for a tunnel junction is that both of the tunneling carriers have low values of effective mass. Here, we take the light-hole mass for holes in CdTe, and the transverse electron effective mass for electrons in Ge (0.08m 0 ). With these values, and with doping densities of 2x10 19 cm -3 on both sides of the junction, the resulting I-V characteristic for the tunnel junction is as shown in Fig. 4. The peak current density is almost two orders of magnitude higher than the Figure 4: I-V characteristic for a p + -CdTe/n + -Ge tunnel junction. Both sides are doped at 1x10 19 cm -3, and the effective masses for holes and electrons are 0.117m 0 and 0.08m 0, respectively. anticipated photocurrent density, and the dynamic specific interface resistivity of the diode at J = J sc is about 5 mωcm 2. Both these properties are indicative of a suitably effective tunnel junction. 4. CONCLUSIONS From this simulation study of CdTe/Ge, thin-film, tandem-junction solar cells it can be concluded that: 1. for satisfactory photocurrent-matching, a p-type absorber in the Ge cell of thickness 3μm must have an electron minority carrier diffusion length of about 10μm, and a back-surface recombination velocity of no greater than about10 3 cm/s; 2. for the formation of an adequate tunnel junction between the CdTe and Ge cells, the doping densities at the heterojunction should be not less than 2x10 19 cm -3. If the above conditions can be satisfied and, of course, if the proven record performance of the CdTe cell can be maintained in the presence of an adjoining thin-film Ge cell, then an improvement in photovoltaic conversion efficiency in excess of 20% appears possible.

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