CORRELATION OF CURRENT MISMATCH AND FILL FACTOR IN AMORPHOUS AND NANOCRYSTALLINE SILICON BASED HIGH EFFICIENCY MUL TI-JUNCTION SOLAR

CELLS

Baojie Yan, Guozhen Yue, Jeffrey Yang, and Subhendu Guha United Solar Ovonic LLC, 1100 West Maple Road, Troy, Michigan

ABSTRACT

We present a systematic analysis of the correlation of current mismatch in a-Si:H/nc-Si:H double-junction solar cell fill factor (FF) measured under colored lights. First, we propose a diagnostic method to evaluate the FFs of component cells in multi-junction solar cells using current-voltage measurements under colored lights. The analysis reveals that the over-estimated FF when a colored light is illuminated results from a significant current mismatch. A mathematical calculation demonstrates that the diagnostic method can be used to estimate the FFs of single-junction component cells in a multi­junction structure. Second, we present our recent progress in the optimization of a-Si:H and nc-Si:H based solar cells. We emphasize the importance of improving the compactness of nc-Si:H materials and contrOlling the nanocrystalline evolution. Finally, we report our new record initial active-area efficiency of 15.4% achieved using an a-Si:H/a-SiGe:H/nc-Si:H triple-junction structure.

INTRODUCTION

Multi-junction structures have been widely used in a-Si:H, a-SiGe:H, and nc-Si:H solar cell designs [1-3]. They offer the following advantages over single-junction structures: the solar spectrum is used more efficiently because the component cells have different bandgaps; the light-induced degradation is reduced because each component cell has a thin intrinsic layer; and the open circuit (or operation) voltage (Voe) is increased. The disadvantages include the requirement of more advanced cell designs and manufacturing processes, and the complexity in the solar cell diagnostics. Since the disadvantages can be mitigated by engineering improvement in the cell design, manufacturing process, and diagnostic tools, multi-junction structures are the dominant cell structures in advanced amorphous and nanocrystalline silicon based thin film solar panel production. In order to achieve high efficiency in multi­junction solar cells, one not only needs to improve the material quality but also optimize the device design. In particular, the current mismatch is a critical parameter for optimizing multi-junction solar cells. In addition, extracting

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component cell properties from the measurements of multi-junction solar cells is an important procedure for diagnostic analysis.

In our previous publications, we have used colored lights to detect the component solar cell characteristics in multi-junction structures [4-5]. This method can provide useful information about component cell performance, especially for sample to sample comparison. However, the fill factor (FF) measured under a short wavelength light is very high. For example, we obtained a FF of 0.82 from an a-Si:H/nc-Si:H double­junction solar cell under an AM1.5 solar simulator with a 585-nm short-pass filter [4]. It is well understood that when a short wavelength light illuminates an a-Si:H/nc-Si:H double-junction solar cell, the bottom cell does not have enough light absorption to create the current to match the top cell current. In this case, the current of the double­junction device is limited by the nc-Si:H bottom cell and the FF measured under this condition shall represent the nc-Si:H bottom cell quality. However, the FF measured under this condition is much higher than what we normally obtain from a nc-Si:H single-junction solar cell. This observation has been puzzling.

In this paper, we present a systematic analysis of component cell FF estimation from multi-junction solar cells under colored lights and propose a method for extracting the component cell FFs. In addition, we present our recent progress in the efficiency improvements with a­Si:H and nc-Si:H based multi-junction solar cells. We focus on the key issues in nc-Si:H component cell optimization, particularly, the improvement of material compactness and control of nanocrystalline evolution. Combining the optimized component cells and multi-junction design, we attained an initial active-area efficiency of 15.4% achieved using an a-Si:H/a-SiGe:H/nc-Si:H triple-junction structure.

EXPERIMENTAL

a-Si:H, a-SiGe:H, and nc-Si:H nip single-junction as well as a-Si:H/nc-Si:H double-junction and a-Si:H/a­SiGe:H/nc-Si:H triple-junction solar cells were deposited using RF and MVHF glow discharges in a multi-chamber system. Bare stainless steel (SS) and AglZnO back reflector coated SS were used as substrates. Indium-Tin­Oxide (ITO) dots with an active-area of 0.25 cm 2 were evaporated on top of p layer as top contacts. Current density versus voltage (J-V) characteristics of component

cells and multi-junction structures were measured under AM1.5 illumination at 25°C. The solar cells were also measured with various neutral density filters and color filters to evaluate the light intensity dependence and the cell performance under different light spectra. Quantum efficiency (QE) curves were measured under short circuit condition for single-conduction cells and under proper optical and electrical biases for multi-junction solar cells in the wavelength between 300 nm to 1100 nm.

DIAGNOSTIC METHOD FOR COMPONENT CELL FF UNDER COLORED LIGHT ILLUMINATION

As previously reported [4], we have used a 585-nm short-pass filter and a 610-nm long-pass filter to evaluate nc-Si:H bottom cells and a-Si:H top cells, respectively, in an a-Si:H/nc-Si:H double-junction structure. Normally, we obtain a FF of over 0.8 under the blue light, and around 0.75-0.78 under the red light. However, we can only obtain a FF of below 0.7 for a nc­Si:H single-junction cell under AM1.5, even for reduced light intensities. To understand this puzzling observation, we have developed the following analytical method.

We first present a qualitatively analysis. It is known that for a multi-junction solar cell, the Jsc is limited by the smallest photocurrent density of the component cells and the Voe is the sum of the values from the component cells for their respective illumination and spectrum. In this case, we ignore the loss at the tunnel junctions, which is a good approximation for optimized multi-junction solar cells. Figure 1 shows two examples of the combination of the J-V characteristics of component cells to form the J-V characteristics of an a-Si:H/nc-Si:H double-junction solar cell, where the component cell J-V data were measured from a-Si:H and nc-Si:H single­junction cells with a multiplication factor used to create the desired current mismatch. At each current value, we added the voltages of the top and bottom cells to obtain the voltage of the double-junction cell. From the top plot of Fig. 1, one can see that when the magnitude of the photocurrent is low, increasing the magnitude of the current caused the voltages of both the top and bottom cells to slightly decrease. When the photocurrent is close to the bottom cell Jse, the top cell voltage does not change too much because the J-V characteristics of the top cell is still very steep, while the voltage of the bottom cell decreases dramatically because it passes the knee point. The corresponding short circuit condition of the double­junction solar cell is that the top cell is under a forward bias, indicated by T, and the bottom cell is under a reverse bias, indicated by B, in Fig. 1. Because the net voltage on the double-junction solar cell is zero, VB must be equal to -VT. In this case, the measured J-V characteristics of the double-junction solar cell is close to the bottom cell J-V characteristics with a right shift of VB to zero. Of course, the no-infinite top cell J-V slope between VT and Voe also affect the double-junction solar cell J-V characteristics. However, when the current mismatch is very large, such as in the measurement with a colored light, the

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contribution of the top cell J-V slope in this region is negligible. In an a-Si:H/nc-Si:H double-junction solar cell, the Voe of the bottom cell is much smaller than the Voe of the top cell; consequently a simplified analysis is that a large rectangle is added to the bottom cell J-V characteristics to form the J-V characteristics of the double-junction solar cell as shown in Fig. 1. Therefore, the J-V characteristics of the double-junction solar cell under a blue light does not directly give the FF of the bottom cell. Instead, a measured curve with a left shift of VT will give a reasonable estimation of the bottom cell FF under a low light intensity.

5 '---~--'-----'------T 5

0

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-10 -11

-15 -15 -1.0 0.0 1.0 2.0

v (V)

5 5

0 0

~ ~

i -5 -5 .5:!

I .., a..

-10 -10

-15 -15 -1.0 0.0 1.0 2.0

v (V)

Fig. 1. Combination of component cell J-V characteristics to form the J-V characteristics of a­Si:H/nc-Si:H double-junction cell. The top plot is the bottom cell limited current mismatch and the bottom one is top cell limited current mismatch.

Table I: J-V characteristic parameters of an a-Si:H/nc-Si:H double-junction solar cell measured under three different r ht Igl s.

Sample # Light Pmax J sc (mW/cm 2) (mAlcm 2)

AM1.5 12.60 11.55 13528-32 <585 nm 1.58 1.64

>610 nm 2.36 2.24

The same analysis is also applicable to the top cell limited current situation as displayed in the bottom plot in Fig. 1. However, the nc-Si:H bottom cell has a smaller Voc than the top cell, therefore the rectangle in the bottom plot is narrower than in the top plot. As a result, the FF measured under the blue light is much larger than under the red light, which does not necessarily imply that the nc­Si:H bottom cell has a better FF than the a-Si:H top cell.

In order to give an easy method for component cell diagnostics from the J-V measurements under various colored lights, we present a simplified mathematical equation. We first define the characteristic parameters of the a-Si:H/nc-Si:H double-junction solar cell: J sc{2b), Voc{2b), FF{2b), Jmax{2b), and Vmax{2b) denote the J sc , Voc, FF, maximum-power current density (J max ) and maximum­power voltage (Vmax) , respectively, under AM1.5 illumination with a 585-nm short-pass filter; Jsc{2r), Voc{2r), FF{2r), Jmax{2r), and Vmax{2r) denote the J sc , Voc, FF, J max ,

and Vmax , respectively, under AM1.5 illumination with a 610-nm long-pass filter. For an a-Si:H single-junction top cell, we define Jsc{Tw), Voc{Tw), FF{Tw), Jmax{Tw), and Vmax{Tw) as J se , Voe, FF, J max , and Vmax , respectively, under a white light illumination that produces the similar current in the top cell of the double-junction structure. The same definition is applied to the nc-Si:H single-junction bottom cell with the parameters of Jsc{Bw), Voc{Bw), FF{Bw) Jmax{Bw), and Vmax{Bw), respectively, for J se , Voc, FF, J max , and Vmax under white light illumination that produces the similar current in the bottom cell of the double-junction structure.

As an example, we consider the situation of an a­Si:H/nc-Si:H double-junction solar cell measured under a 585-nm short-pass filter and try to find the correlation of the colored FF of the double-junction cell and the FF of the nc-Si:H single-junction bottom cell under a similar light intensity as in the double-junction cell. The same logic applies to the situation of illumination with a red light. Because, under the filtered light, a very large current mismatch is created, we assume that the shape of the J-V characteristics of the double-junction cell is the J-V

Table II: Estimated FFs of a-Si:H top cell and nc-Si:H bottom cell from the a-Si:H/nc-Si:H double-junction cell measured under colored li!lhts. Light FF Voe {2b) Vmax {2b) Voe(TW) FF{Bw)

or or or or Voe{2r)

M Vmax {2r)

M Voe{Bw)

M FF(TW)

<580 0.833 1.36 1.23 0.90 0.66 nm >610 0.768 1.36 1.18 0.35 0.73 nm

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Voe FF J max Vmax

M (mAlcm 2) M 1.45 0.750 11.35 1.11 1.36 0.833 1.51 1.23 1.36 0.774 2.01 1.18

characteristics of the single-junction bottom cell (under a white light that generates the same J sc as in the double­junction cell) adding a rectangle with a height of Jsc{Tw) and width of Voc{Tw) of a-Si:H top-junction cell under the white light that generates the same J sc as in the double­junction cell. Under these conditions, we have Jmax{Bw)=Jmax{Tw)= Jmax{2b) and Jsc{Bw) =Jsc{Tw) =Jsc{2b). In addition, we assume that Vmax{Bw)=Vmax{2b)-Voc{Tw). Although, theoretically this assumption is not absolutely correct, the error from the assumption is very small with the confirmation from numerical calculation. Based on the above assumptions, we obtain the following equation:

FF(Bw) = Jmax{Bw)Vmax{Bw) J sc (Bw)Voc (Bw)

_ J max (2b){Vmax (2b)- Voc{Tw)) - J sc {2b XVoc (2b) - VoJTw))

J (2b)V (2b{1- Voc{TW)J max max \ Vmax (2b)

= J {2b)V (2b)(1- Voc (TW)J

sc oc Voc (2b)

(1- VoJTW)J

= FF(2b) Vmax (2b)

(1- Voc{TW)J Voc (2b)

(1 )

Similarly, we obtain the equation for the situation of a strong top cell limited current mismatch under the red light illumination (>610 nm):

FF(Tw) = FF(2r) ( ()J . 1- Voc Bw

Voc (2r)

(2)

Table I lists a set of J-V characteristic parameters from an a-Si:H/nc-Si:H double-junction solar cell measured under the three lights: AM1.5, AM1.5 with a 585-nm short­pass filter, and AM1.5 with a 610-nm long-pass filter. One notices that the FF under the blue light is 0.833, which is larger than that under the red light. We used the estimation method of eq.(1) and eq.(2) to calculate the FF of the component cells. The results are listed in Table II. The estimated FF of the nc-Si:H bottom cell is 0.66, which is very close to the number obtained from a nc-Si:H single­junction solar cell. Similarly, the estimated FF of the a-Si:H top cell is very reasonable.

We should point out that the calculation of the component cell FF is a rough estimation because there are two simplifications. First, the subtraction of a rectangle from the double-junction J-V characteristics ignores the given slope (assumed a vertical line) of the non-limiting cell J-V characteristics between the small current region. Second, the Voc and Vmax of the non-limiting cells are estimated or obtained from single-junction solar cells under a reduced light intensity. However, the estimated FFs of the component cells are similar to those obtained from single-junction measurements. This result provides a clear understanding for the puzzling result of very high FF from a multi-junction solar cell with a nc-Si:H bottom cell measured under blue light. Although, this method may not provide a very accurate FF of the component cells, as a quick diagnostic method, the measurement of J-V characteristics under colored light is a very easy and useful method.

HIGH EFFICIENCY MULTI-JUNCTION

In order to obtain high efficiency multi-junction solar cells, the component cells must be first optimized. United Solar has significant knowledge in the optimization of a-Si:H and a-SiGe:H single-junction solar cells and achieved high efficiency in a-Si:H/a-SiGe:H/a-SiGe:H and a-Si:H/a-SiGe:H/nc-Si:H triple-junction structures [1,4,5]. For example, Fig. 2 shows the improvement of a-Si:H solar cell Voe at United Solar, where a nanocrystalline p layer and high hydrogen dilution were the most important techniques used to increase the Voe. In particular, using hydrogen dilution profiling to reach to the edge of amorphous/nanocrystalline transition through the whole intrinsic layer thickness has resulted in a Voc of 1.055 V.

~ ;;

1.10 I Near the edge I .. I High H2 dilution I """-

1.05

1.00

Nanocrystailine player

0.95

0.90

0.85

0.80 -0.75

1980 1985 1990 1995 2000 2005 2010

Year

Fig. 2. The improvement of Voc by different technologies.

The a-SiGe:H middle cell is very important for high efficiency triple-junction solar cells. The optimization of the a-SiGe:H component cell includes several critical processes such as band gap profiling, hydrogen dilution profiling, and optimizing Ag/ZnO back reflector. Table III lists an example of contributions from each step. The solar cells were measured under an AM1.5 solar simulator for efficiency measurements and under the solar simulator with a 610-nm long-pass filter to simulate the performance in triple-junction structures. One can see that under optimized conditions, a-SiGe:H single-junction middle cells show an initial active-area efficiency over 10.5% and the long wavelength maximum power (P max ) is over 5 mW/cm 2.

The most critical component cell for high efficiency a-Si:H/nc-Si:H double-junction and a-Si:H/a­SiGe:H/nc-Si:H triple-junction solar cell is the nc-Si:H bottom cell. First, nc-Si:H films normally have certain degree of porosity. Small angle X-ray scattering measurements found the micro-void density could be as

Table III. Typical J-V characteristics of a-SiGe:H middle cells on Ag/ZnO back reflector for a-Si:H/a-SiGe:H/nc-Si:H triple-junction structures, where the measurements under the 610-nm long-pass filter simulate the cell performance in trip Ie-junction structures.

Optimization Light Jse Voc FF Pmax (mAlcm 2) M (mW/cm 2)

Baseline AM1.5 19.94 0.775 0.597 9.23 >610 nm 8.85 0.743 0.613 4.03

Bandgap AM1.5 20.52 0.761 0.608 9.45 Profiling >610 nm 9.46 0.731 0.598 4.14 Pressure AM1.5 20.84 0.753 0.606 9.51

>610 nm 9.92 0.724 0.605 4.35 H2 dilution AM1.5 21.21 0.760 0.632 10.19

>610 nm 10.18 0.730 0.637 4.73 Improved AM1.5 22.07 0.763 0.627 10.56

Ag/ZnO BR >610 nm 10.92 0.735 0.629 5.05

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1.E+22

~ 1.E+21

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1.E+17

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Depth (mm)

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Fig. 3. Oxygen profiles in nc-Si:H/a-Si:H multi-layer structures. In (a), the sample was made with nc-Si:H/a­Si:H/nc-Si:H triple-layers. In (b), the sample was made with nc-Si:H/a-Si:H double layers, where the nc-Si:H is more compact than that in (a).

higher as 3-6 vol.% in non-optimized nc-Si:H films [6]. The high porosity caused an ambient degradation in nip solar cells, where the nc-Si:H solar cell performance decreased as a function of time without intentional light soaking [7]. We have identified that the ambient degradation was caused by impurity diffusion. Figure 3 shows a comparison of oxygen profiles on two nc-Si:H/a-Si:H multi-layer structures. In Fig. 3 (a), the first layer from the left is a non­optimized nc-Si:H film, the middle layer is an a-Si:H film, and the layer on the right is the same as the left one. It is clear that there was a significant oxygen diffusion into the first nc-Si:H layer and the middle a-Si:H layer blocked the impurity diffusion. The oxygen content in the bottom nc­Si:H layer was around 3-5x10 18 at.lcm 3. The first layer in Fig. 3 (b) is an optimized nc-Si:H layer with a compact structure, where the diffusion tail near the surface is very narrow, indicating a compact structure with reduced impurity diffusion. nc-Si:H single-junction solar cells made with the optimized nc-Si:H did not show measurable ambient degradations.

Fig. 4. X-TEM image a nc-Si:H solar cell made with a hydrogen profile on bare stainless steel substrate.

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The second important aspect in nc-Si:H solar cells is nanocrystalline evolution, where the crystallinity increases with film thickness associated with nanocrystalline cone formation and growth. We have

5 (a)

0

-5

'] -10

~ - -15 ...,

-20

-25

-30 -0.2 0

Eff=9.23 %

Jsc=27.62 mA/cm2

Voc=O.529 V

FF=O.632

Active area=O.25 cm2

0.2

v (V)

0.4 0.6

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0.8

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0.4

0.3

0.2

0.1

(b) 27.62 mA/cm2

0.0 +---~~-~-~-~-~-~~ 300 400 500 600 700 800 900 1000 1100

Wavelength (nm)

Fig. 5. (a) J-V characteristics and (b) quantum efficiency curve of a nc-Si:H single-junction cell with an initial active-area efficiency of 9.23%.

2

0

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Wavelength (nm)

Fig 6. (a) J-V characteristics and (b) quantum efficiency curves of an a-Si:H/a-SiGe:H/nc-Si:H triple-junction cell with an initial active-area efficiency of 15.4%.

developed a hydrogen dilution profiling technique to control the nanocrystalline evolution [8]. As a result, we nanocrystalline volume fraction is very uniform along the growth direction as shown in Fig. 4, where no amorphous incubation layer and nanocrystalline cone formation were observed. In addition, the cell structure is also very important, especially the optimization of nIi and i/p buffer layers [9]. Combining the optimization of nc-Si:H material structure and device design, we attained an initial active­area area efficiency of 9.2% using a nc-Si:H single­junction solar cell with a very good long wavelength response as shown in Fig. 5, where the J sc is over 27 mAlcm 2 obtained by the convolution integral of the QE curve with AM1.5 solar spectrum.

We have incorporated the optimized a-Si:H, a­SiGe:H, and nc-Si:H component cells into triple-junction structures and optimized the cell design. The highest initial active-area cell efficiency of 15.4% is achieved with the J­V characteristics and quantum efficiency shown in Fig. 6.

SUMMARY

We have developed a method for investigating component cell FFs in multi-junction solar cells. The method includes J-V measurements under colored lights with a mathematical calculation. We presented the optimizations of a-Si:H. a-SiGe:H, and nc-Si:H component cells for high efficiency multi-junction solar cells. We found that improving material compactness and controlling the nanocrystalline evolution are the two most important aspects of the nc-Si:H solar cell optimization. Finally, we report an initial active-area efficiency of 15.4% achieved using an a-Si:H/a-SiGe:H/nc-Si:H cell structure.

ACKNOLEDGEMENTS

This work was supported by US DOE under Solar America Initiative (SAl) Program with contract No. DE-

978-1-4244-1641-7/08/$25.00 ©2008 IEEE

FC36-07 GO 17053. The authors thank the dedicated work at the R&D group of United Solar Ovonic LLC.

REFERENCES

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[3] S. Fukuda, K. Yamamoto, A. Nakajima, M. Yoshimi, T. Sawada, T. Suezaki, M. Ichikawa, Y. Koi, M. Goto, T. Meguro, T. Matsuda, T. Sasaki, and Y. Tawada, Proc. of 21 st European Photovoltaic Solar Energy Conference, (2006, Dresden, Germany), p.1535.

[4] B. Yan, G. Vue, J. Yang, A. Banerjee, and S. Guha, Mater. Res. Soc. Symp. Proc. 762, 309 (2003).

[5] G. Vue, B. Van, G. Ganguly, J. Yang, S. Guha, C. W. Teplin, and D.L. Williamson Record of the 4th World Conference on Photovoltaic Energy Conversion (2006. Hawaii, USA), p1588.

[6] D. L. Williamson, Solar Energy Materials & Solar Cells 78,41 (2003).

[7] B. Yan, K. Lord, J. Yang, S. Guha, J. Smeets, and J­M. Jacquet, Mater. Res. Soc. Symp. Proc. 715, 629 (2002).

[8] B. Van, G. Yue, J. Yang, S. Guha, D. L. Williamson, D. Han, and C.-S. Jiang, Appl. Phys. Lett. 85, 1955 (2004).

[9] G. Vue, B. Van, C. W. Teplin, J. Yang, and S. Guha, J. Non-Crystal Solids 354,2440 (2008).