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): pulfrey@ece.ubc.ca
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 extensively1-3. 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 well4,5. 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 market6.
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 20043. 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 CdZnTe7 or
CdMgTe8); using graded bandgap structures4; utilizing tandem cells based on combinations of II-VI materials (for
example CdTe and CdHgTe9). 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 demonstrated10, 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 cell11, 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. 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 regions12. 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 cell3. 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: CdTe13 and Ge14. 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 Wu3 and the CdTe cell used in our simulations.
Jsc (mA/cm2)
25.88
25.89
Wu
Our model
Voc (mV)
845
845
FF
0.755
0.778
PV efficiency (%)
16.5
17.0
Table 2: Regional parameters for each cell: front-surface reflectivity, surface recombination velocities, doping densities, regional
widths, minority carrier diffusion lengths.
Reflectivity (%)
CdTe
Ge
6.5
0
S F, S B
(cm/s)
5x104, 1x107
1x103, 1x103
Nd, Na
(cm-3)
18
1x10 , 1x1015
1x1019, 2x1017
xemitter, xabsorber
(micron)
0.1,
2.5
0.1,
3.0
L e, L h
(micron)
0.65, 0.23
10,
1
regions15.
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 capability16.
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 2x1019 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 -0.88 eV17.
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/cm2, 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.
Ge alone
CdTe/Ge tandem
Jsc (mA/cm2)
25.8
25.8
Voc (mV)
268
1113
FF
0.700
0.762
21.8%, i.e., to an improvement of 28% over that of the stand-alone CdTe cell listed in Table 1.
PV efficiency (%)
4.8
21.8
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 Palik18.
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.
SF (cm/s)
SB (cm/s)
Le (micron)
Voc (mV)
Jsc (mA/cm2)
Ge PV
efficiency (%)
1x103
1x107
1x103
1x107
1x107
1x107
1x103
1x103
1x103
1x104
1x105
1x107
10
10
5
10
50
50
1113
1099
1085
1078
1055
1047
25.8
24.2
24.8
22.9
20.2
18.9
4.8
4.2
4.0
3.6
2.8
2.5
Efficiency
improvement
(%)
28
22
22
16
2
-4
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 1x1019 cm-3. For example, NV(CdTe) = 9.4x1018
cm-3, based on heavy- and light-hole masses of 0.485m0 and 0.117m0, respectively19. While extremely high p-type
doping of CdTe (hole concentration of 5x1019 cm-3) has been demonstrated using ion implantation and pulsed electron
beam annealing20, 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 (0.08m0). With these
values, and with doping densities of 2x1019 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 1x1019 cm-3, and the effective masses for
holes and electrons are 0.117m0 and 0.08m0, respectively.
anticipated photocurrent density, and the dynamic specific interface resistivity of the diode at J = Jsc is about 5 mΩcm2.
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.
2.
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
about103 cm/s;
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 2x1019 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.
REFERENCES
[1] Aberle, G., “Thin-film solar cells,” Thin Solid Films 517(17), 4706-4710 (2009).
[2] Diehl, W., Sittinger, V. and Szyszka, B., “Thin film solar cell technology in Germany,” Surface and Coatings
Technology 193(1-3), 329-334 (2005).
[3] Wu, X., “High-efficiency polycrystalline CdTe thin-film solar cells,” Solar Energy 77(6), 803-814 (2004).
[4] Dharmadasa, M., “Latest developments in CdTe, CuInGaSe2 and GaAs/AlGaAs thin film PV solar cells,” Current
Applied Physics 9(2), e2-e6 (2009).
[5] Böer, K.W., “CdS enhances Voc and fill factor in CdS/CdTe and CdS/CuInSe2 solar cells,” J. Appl. Phys. 107,
023701 (2010).
[6] Stevenson, R., “First Solar: Quest for the $1 Watt,” IEEE Spectrum Online,
http://spectrum.ieee.org/energy/renewables/first-solar-quest-for-the-1-watt (2008).
[7] Shafarman, W. and McCandless, B., “Development of a wide bandgap cell for thin film tandem solar cells,” Final
Technical Report, NREL/SR-520-42388, available from http://www.osti.gov/bridge/servlets/purl/937358-cfuA0e/
(2008).
[8] Mathew, X., et al., “Development of a semitransparent CdMgTe/CdS top cell for applications in tandem solar cells,”
Semicond. Sci. Technol. 24(1), 015012 (2009).
[9] Parikh, V., et al., “Hg1-xCdxTe as the bottom cell material in tandem II-VI solar cells,” Thin-Film Compound
Semiconductor Photovoltaics”, Mater. Res. Soc. Symp. Proc. 1012, Y12-37 (2007).
[10] Tsao, C.-Y., “Low-temperature growth of polycrystalline Ge thin film on glass by in situ deposition and ex situ
solid-phase crystallization for photovoltaic applications,” Appl. Surf. Sci. 255(15), 7028-7035 (2009).
[11] Coutts, T.J., et al., “Critical issues in the design of polycrystalline, thin-film tandem solar cells,” Prog. Photovolt:
Res. Appl. 11(6), 359-375 (2003).
[12] Pulfrey, D.L., “Understanding Modern Transistors and Diodes,” Cambridge University Press, 120-125 (2010).
[13] Gloeckler, M., Fahrenbruch, A.L. and Sites, J.R., “Numerical Modeling of CIGS and CdTe Solar Cells: Setting the
Baseline,” Proc. World Conf. on Photovoltaic Energy Conversion 3, 491-494 (2003).
[14] Friedman, D.J. and Olson, J.M., “Analysis of Ge junctions for GaInP/GaAs/Ge three-junction solar cells”, Prog.
Photovolt: Res. Appl. 9(3), 179-189 (2001).
[15] Hovel, H., “Semiconductors and Semimetals, Vol. 11: Solar Cells,” Academic Press, 50-52 (1975).
[16] Hermle, H., et al., “Numerical simulation of tunnel diodes for multi-junction solar cells,” Prog. Photovolt: Res.
Appl. 16(5), 409-418 (2008).
[17] Katnani, A.D. and Margaritondo, G., “Microscopy study of semiconductor heterojunctions: Photoemission
measurement of the valance-band discontinuity and the potential barriers,” Phys. Rev. B 28(4), 1944-1956 (1983).
[18] Palik, E.D., Handbook of Optical Constants of Solids, Vol.1, Academic Press, 472-478 (1997).
[19] B. Kuhn-Heinrich et al., “Determination of the band offset in semimagnetic CdTe/Cd1-xMnxTe quantum wells: a
comparison of two methods,” J. Appl. Phys. 75(12), 8046-52 (1994).
[20] Hwang, H.L., Hsu, K.Y.J. and Ueng, H.Y., “Fundamental studies of p-type doping of CdTe,” J. Cryst. Growth,
161(1-4), 73-81 (1996).