White Paper To Mok- Final-1

Technical Report Optimization of Multi-Junction Solar Cells For Operation Inside Ultra-High Concentration Photovoltaic (UHCPV) Module October 19, 2004 Submitted to Mok Industries As the final deliverable under Spectrolab Sales Order # 5926 Prepared By Raed A. Sherif, Ph.D. Manager, Terrestrial Photovoltaic Products Phone (818) 838-7479 [email protected] Hector L. Cotal, Ph.D. Photovoltaic Research Scientist Richard R. King, Ph.D. Manager, Solar Cell Research & Development

1 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

TABLE OF CONTENTS

1.0 Background

Page 3

2.0 Performance Optimization of Triple-Junction Solar cells 2.1 Gridline Optimization 2.2 Tunnel Junctions 2.3 Optimum Solar Cell Total Area 2.4 Thermal Effects on the Maximum Power 2.5 Wafer Power Output 2.6 Heat Reduction from Attenuation of Incident Solar Spectrum

Pages 4-14

3.0 Performance Optimization of Dual-Junction Solar Cells 3.1 Thermal Effects on the Maximum Power 3.2 Wafer Power Output

Pages 15-17

4.0 Product & Process Improvements 4.1 Tunnel Junction Improvements 4.2 Pursuit of Higher Cell Efficiencies 4.2.1 Metamorphic Solar Cells 4.2.2 Solar Cells with 4, 5, and 6 Junctions 4.3 Scribe & Break Process Development 4.4 Reducing the Ge Wafer Cost

Pages 18-23

5.0 Concentrator Cells Cost Projection

Pages 24-25

6.0 Summary & Conclusions

Page 26

2 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

1.0 Background High concentration photovoltaic (HCPV) modules using high-efficiency multijunction (MJ) cells have been sought because they have the potential of generating electricity at competitive prices. The key to generating cheap electricity from HCPV modules is to increase the module output per a given collector area without increasing the area of the (more expensive) semiconductor. Hence, the cell efficiency is a critical parameter in reducing the cost of the overall module ($/Watt). Equally important is how much concentrated sunlight can the solar cell take without causing degradation to its performance. As the concentration level on the cell increases, heat dissipation becomes more demanding. The tunnel junction inside the cell will be more likely to fail as the current density increases beyond a certain level. Further, series losses at the higher current levels may cause the cell to operate below its intended peak efficiency. Mok Industries seeks to develop Ultra-High Concentration Photovoltaic (UHCPV) modules. This study is funded by Mok Industries and is intended to address issues associated with operation of MJ cells under concentration levels between 1000 to 5000 suns. Specific issues related to this are: solar cell performance optimization, heat dissipation, and economics. In this study, we consider performance optimization of triple-junction solar cells. We also consider optimization of dual-junction cells. In both cases we consider the impact of filtering part of the infrared (IR) radiation so that less thermal energy is absorbed in the solar cell (reducing the amount of heat that will need to be dissipated).

3 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

2.0

Performance Optimization of Triple-Junction Solar Cells

Performance optimization for the solar cells under any concentration level requires optimization of the cell front grid lines (so that there is enough metal to carry the current without incurring too much I2R losses, but not too much metal so as to keep the obscuration losses to a minimum too). Under ultra-high concentration, e.g., 1000-5000 suns, the tunnel junctions inside the solar cells also need to be optimized to ensure that proper tunnel junctions with high peak tunneling currents are used to support the high current densities generated within the electrically active junctions. Under concentration levels of 1000-5000 suns, it is expected that temperature effects will likely dictate how large the solar cell can be, for it can be practically impossible to cool down the cells if the cell area is in the order of 1cm x 1cm. In this study, we will focus our attention on performance optimization of today’s GaInP/GaInAs/Ge triple-junction cells whose cross-section is shown in Fig. 1. We will consider cell sizes that are under 0.3cm x 0.3cm. This is guided by the results of the thermal analysis and by some power calculations that will be discussed at later sections. contact AR n+-Ga(In)As n-AlInP window n-GaInP emitter

GaInP top cell

p-GaInP base

p-AlGaInP BSF

Wide-bandgap tunnel junction

p++-TJ n++-TJ

i W

g -E de

n-GaInP window n-Ga(In)As emitter

Ga(In)As middle cell

p-Ga(In)As base

M

p-GaInP BSF

Tunnel junction Buffer region

p++-TJ

Tu

Tu

e dl id

n

el nn

C

un lJ ne

l

l el

n io ct

n++-TJ

n-Ga(In)As buffer

nucleation

n+-Ge emitter

Ge bottom cell

el C

p To

p-Ge base and substrate

m tto Bo

l Ce

l

contact

Fig. 1: Cross-Section of a triple-junction solar cell

2.1 Gridline Optimization This entails computing a number of loss components that affect the power output of the cell such as the amount of metal deposited on the front surface, its obscuration (or shadowing), sheet resistance across the plane of the front face of the semiconductor, I2R heating through gridlines and bus bar(s), contact 4 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

resistance between the front metal and the semiconductor and tunnel junction losses. Figure 2 shows a graph of the relative power loss of triple junction concentrator solar cell for 1000, 3000 and 5000 suns for a 0.1cm x 0.1cm cell. 100

Fractional Power Loss (%)

Total Cell Area = 0.1 cm x 0.1 cm

80 5000 Suns

3000 Suns

1000 Suns

60

40

20

0 0

50

100

150

200

250

300

Gridline Spacing (µm)

Fig. 2: Triple-Junction solar cell grid line optimization for a 0.1cm x 0.1cm cell

The plot for 1000 suns shows that the grid pitch (or separation) should be 157.5 µm apart for the solar cell to attain a combined minimum loss in power. For this case, the total power loss is 15.34% and can be considered as the percentage loss relative to a solar cell with “ideal” 0% loss. At 3000 suns, the power loss increases to 24.69% with a 96.5 µm-pitch, and at 5000 suns, the loss rises to 30.65% with a 76.2 µm-pitch. Bus Bar Included in the calculations was a bus bar width that was selected as 60 µm and remain fixed throughout the calculations. The length was allowed to vary but the width was selected so that it would be narrow enough to minimize obscuration and large enough to allow wire bonding. Some wire bonding characteristics will be described below. Gridline Width The modeling was performed with the narrowest gridline width possible as allowed by Spectrolab’s current processing capabilities. Note that narrow gridline width reduces obscuration of which is a significant loss mechanism for the small cells modeled in this study. To achieve further reduction in gridline width, the photolithography process would have to be modified to account for narrow gridline width fabrication. 5 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

Sheet Resistance An important parameter that contributes to power loss at high concentration levels is the sheet resistance. The plots in Fig. 2 are based on a sheet resistance of 500 Ω/square. Figure 3 shows how smaller values of the sheet resistance can affect the power loss. The difference in power loss between 500 Ω/square and 100 Ω/square is 3.5%. For 3000 and 1000 suns the difference becomes 2.9% and 1.8%, respectively. 100

Fractional Power Loss (%)

5000 SUNS MODEL Sheet rho = 500 Ohms/sq

80

Sheet rho = 250 Ohms/sq Sheet rho = 100 Ohms/sq

60

Total Cell Area = 0.1 cm x 0.1 cm

40

20

0 0

50

100

150

200

250

300

Gridline Spacing (µm)

Fig. 3: The effect of sheet resistance on the fractional power loss of a triple-junction solar cell.

Contact Resistance Values of ρc for the plots in Figs 2 and 3 were based on a value of 2x10-4 Ω cm2. Several values that ranged from 2x10-4 Ω cm2 to 5x10-6 Ω cm2 were included in the models for the 1000, 3000 and 5000 suns for comparison. Significant changes in the power loss were observed for values of ρc below 2x10-4 Ω cm2, and were more pronounced for the modeled case of 5000 suns, which is shown in Fig. 4. Values of ρc for 1000, 3000 and 5000 suns are illustrated in Table 1. The end result is that ρc needs be reduced by at least an order of magnitude to achieve higher solar cell performance. Table 1: Power loss as a function of contact resistance for 1000, 3000, and 5000 suns concentration Concentration % Power Loss Contact Resistance Values (Ω cm2) 2x10-4 1x10-5 5x10-6 1000 15.34 7.90 5.50 3000 24.69 12.68 8.67 5000 30.65 15.83 10.77 6 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

50

Fractional Power Loss (%)

5000 SUNS MODEL

40

Cont Res = 0.0002 Ohms cm2 Cont Res = 0.00001 Ohms cm2

30

Cont Res = 0.000005 Ohms cm2

Total Cell Area = 0.1 cm x 0.1 cm

20

10

0 0

50

100

150

200

250

300

Gridline Spacing (µm)

Fig. 4: Noticeable change in the total power loss with increasing contact resistance at 5000 suns.

Wire Bond Pad Resistance The modeling took into account the pad resistance of the gold wire bond for typical FP2 25 µm diameter wire as described on Kulicke & Soffa (KnS) Industries web site. The wire bond pad resistance is < 1 Ω. There are many types of wires of different material. Gold is selected in this study for compatibility since the topmost front metal layer of the solar cell bus bar is normally comprised of gold. The wire electrical resistivity as referenced in KnS site is 3.24 µΩ-cm. Spectrolab has demonstrated that wire bonding is a viable method to use for concentrator solar cells in the past. 2.2

Tunnel Junctions

The solar cell structure is grown in the Metal Organic Vapor Phase Epitaxy (MOVPE) reactors. The epitaxial layers grown in the MOVPE reactors must balance the peak current output from each electrically active junction (since each subcell of the triple-junction cell are in series). Each pair of junctions is bridged by a tunnel-junction allowing current to flow with ease between the electrically active junctions. The primary characteristic of a tunnel junction is its peak tunneling current. This is the maximum current density for which a tunnel junction operates without severely hindering cell performance. Current flow between each pair of electrically active junctions is limited by the peak current density (Jp) of the tunnel junction. Figure 5 illustrates a graph approximating the tunnel junction 7 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

characteristics in the present tunnel junction used in the triple-junction structure. The Jp from this particular tunnel junction is approximately 75 A at 0.16 V. 100

Peak Current ≡ J p

2

J (A/cm )

80

60

40 0.10 V;

20

2

69 A/cm

0 0

0.5

1

1.5

2

V (V)

Fig. 5: Tunnel junction characteristics in a triple-junction cell (plot is for Eg = 1.9-2.0 eV)

For a concentrator cell operating at 5000 suns, the current density at maximum power (Jmp) for this cell design is 69 A/cm2. In Fig. 5, the voltage drop that corresponds to this Jmp is about 0.10 V, and would be manifested in the form of power loss in the cell performance due to this component. Although the voltage drop is somewhat low, its Jp is not high enough as Jp should be 2- but preferably 3-times higher than Jmp of 69 A/cm2. Since variations in the growth of tunnel junctions can occur, these factors give a margin of safety to compensate for such variations. Since Jp is low, this particular tunnel junction would not be suitable for a concentrator cell at 5000 suns. (This was confirmed experimentally by studies done with concentrated light coming out of a fiber shining light on smaller areas of the cell. Occasional tunnel junction failures were reported at concentration levels slightly above 2200 suns.) It is clear that we need to define a tunnel junction that has peak tunneling current of at least 140 A/cm2 (but preferably higher than 200 A/cm2). The peak tunneling current is dependent on the band gap (Eg) of the semiconductor: the lower the Eg, the higher the Jp. The choice of Eg, however, is one where Eg should be low enough to allow for high Jp (and low voltage drops) but high enough to reduce light absorption in the tunnel junction. The plot in Fig. 5 is representative of a tunnel junction with Eg of 1.9 to 2.0 eV. Some tunnel junctions that fall in the category of high Jp and low Eg could be the AlGaAs/InGaAlP, AlGaAs/GaInP and AlGaAs/GaAs ternary and quarternary 8 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

systems. By proper adjustment of the Aluminum, Gallium and Indium compositions, the desired tunnel junctions with lower Eg can be developed with Jp above 200 A/cm2. This is clearly a development effort that must be undertaken by Spectrolab in any future work with Mok Industries to make multi-junction cells operate reliably under concentrations of 3000-5000 suns. 2.3 Optimum Solar Cell Total Area It is important to keep in mind that when it comes to heat removal from a device, there are two parameters to consider: (a) the power density expressed as W/cm2, and (b) the magnitude of the power itself in Watts.

Cell Temperature above ambient (deg. C)

Concentration levels of 1000-5000 suns correspond to approximately 70-350 Watts/cm2 (assuming 30% cell conversion efficiency). These are extremely high numbers in terms of power density that will be very difficult to remove while maintaining a reasonable cell operating temperature (preferably below 100 deg. C) with passive cooling. Fortunately, however, by keeping the cell size very small, the absolute value of power is still manageable. Figure 6 shows a plot of the projected cell operating temperature rise above ambient vs. levels of concentration for different cell sizes (assuming 1 sun = 1000 W/m2 and that the cell conversion efficiency is 35%).

160 140 120 1mmx1mm cell 2mmx2mm cell 3mmx3mm cell

100 80 60 40 20 0 0

2000

4000

6000

Concentration

Fig. 6: Finite element projections of cell temperature rise above ambient for different cell sizes under different concentration

9 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

The data in this curve are based on a 3-dimensional finite element model that assumes the cell to be soldered directly to a heat spreader made of copper. Direct soldering of the cells to Cu is usually not practiced for larger cells (e.g., 1cm x 1cm) since the coefficient of thermal expansion (CTE) of Cu is much higher than that of the MJ cell. Under repeated temperature cycling, large expansion mismatch can lead to breakage of the cell and/or the solder joint between the cell and the heat spreader (leading to loss of cooling and thermal runaway). For smaller cell sizes, however, direct boding can take place without incurring too much thermal stresses. The heat spreader has dimensions of 5cm x 5cm and its thickness is 0.2cm. Heat removal from the back of the heat spreader occurs by natural convection (i.e., passive cooling) with the heat transfer coefficient assumed to be 100 W/m2-deg C, which is typical of natural heat convection. From the curves in Fig. 6, it is clear why the cell size should be limited to under 2mm x 2mm under concentration above 3000 suns. Another factor to consider in the selection of cell area is the current level produced by the cell. Smaller cells will have smaller current generated and, hence, smaller I2R losses). Figure 7 shows the power loss vs. the total solar cell area for 1000, 3000 and 5000 suns. 40 1000 Suns

% Power Loss

35

3000 Suns

5000 suns

30 25 20 15

Minimum Power Loss

10 0

0.01

0.02

0.03

0.04

0.05

0.06

2

Total Cell Area (cm )

Fig. 7: Power loss vs. total cell area at different concentration

10 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

2.4

Thermal Effects on the Maximum Power

Higher operating cell temperature reduces the cell conversion efficiency, which occurs mostly because of reduction in cell operating voltage. The dependence of Vmp on temperature plays a crucial role on the performance of concentrator solar cells. If heat is not dissipated adequately, Vmp will drop and the power output of the cell will also drop. Table 2 shows the expected drop in cell voltage and power as temperature goes up. The data is based on experiments conducted at Spectrolab for concentrator cells 0.55cm x 0.55cm with the maximum current (Imp) scaled to the 0.1cm x 0.1cm and 0.2cm x 0.2cm cells. Table 2: The effect of temperature on Vmp and power at 1000 suns. Imp = 0.516A for 0.2cm x 0.2cm and Imp = 0.121A for 0.1cm x 0.1cm Parameter Operating Temperature (oC) 25 45 65 85 Vmp (V) 2.68 2.59 2.50 2.41 Pmp (W) 0.32 0.31 0.30 0.29 Cell A =0.1cm x 0.1cm Pmp (W)

Cell A =0.2cm x 0.2cm

1.38

1.34

1.29

1.24

Please note that the temperature coefficient of Imp has been ignored for the calculations in Table 2, as it is much smaller than the impact of temperature on voltage. 2.5 Wafer Power Output Previous discussions focused on individual cells. The smaller the cells, the easier the heat dissipation is and the smaller the I2R losses are. In smaller cells, however, the ratio of the bus bar to the active cell area is larger; hence, on a wafer level, smaller cells will correspond to larger loss of wafer active area (and hence lower power). Since the ultimate objective of any concentrating PV system is to reduce the cost of electricity generation ($/Watt), the wafer power output must be taken into account when deciding on the optimum cell area. A 10cm diameter Ge wafer is used for growing epitaxial layers to form the terrestrial concentrator structure. If we eliminate the unusable wafer area (about 3mm from the outer edge of the wafer), then we can obtain: - 0.1cm x 0.1cm cells total = 6,219 cells per wafer - 0.2cm x 0.2cm cells total = 1,613 cells per wafer

11 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

At 5000 suns, assuming 25 C cell operation (which is impractical to achieve in actual module operation, but represents standard test conditions), the following power is achieved from each cell and wafer. Standard Test Condition Power of 0.1cm x 0.1cm cell = (Imp = 0.52A) x (Vmp = 2.68V) = 1.4 Watts/cell Power of a whole wafer = 1.4 (W/cell) x 6,219 (cells/wafer) = 8.67 kW/wafer Power of 0.2cm x 0.2cm cell = (Imp = 2.22A) x (Vmp = 2.68V) = 5.95 Watts/cell Power of a whole wafer = 5.95 (W/cell) x 1,613 (cells/wafer) = 9.60 kW/wafer This clearly favors the use of the larger cell (the 0.2cm x 0.2cm) over the smaller cell (the 0.1cm x 0.1cm). In actuality, however, the smaller cell will operate at lower temperature, as suggested by Fig. 6. Including the temperature effects (and assuming 25 deg. C ambient), we obtain the following power. Real Temperature Test Condition Power of 0.1cm x 0.1cm cell = (Imp = 0.52A) x (Vmp = 2.59V) = 1.35 Watts/cell Power of a whole wafer = 1.35 (W/cell) x 6,219 (cells/wafer) = 8.38 kW/wafer Power of 0.2cm x 0.2cm cell = (Imp = 2.22A) x (Vmp = 2.35V) = 5.22 Watts/cell Power of a whole wafer = 5.22 (W/cell) x 1,613 (cells/wafer) = 8.42 kW/wafer In other words, the fact that the smaller cell will operate at lower temperature made the use of either cell almost equivalent in terms of total wafer power. 2.6 Heat Reduction from Attenuation of Incident Solar Spectrum It was found from the above analysis that if the temperature were the same, a 0.2cm x 0.2cm cell will be more favorable to 0.1cm x 0.1cm cells (resulting in higher power per wafer). In this section, we investigate ways of reducing the amount of thermal radiation by cutting off the unusable (and some of the usable portion) of incident infrared (IR) in the terrestrial spectrum. Figure 8 shows the AM1.5G terrestrial spectrum along with the spectral response of each subcell in the triple junction solar cell. It can be seen that the GaInP/GaInAs/Ge triple-junction solar cell uses most of the spectrum from 350 to 1900 nm. Since there is no absorption, and therefore no contribution to current generation above 1900 nm, this portion of the IR can be cut off or filtered with no effect on solar cell performance. Calculation of the irradiance of this portion of the unusable spectrum at 1-sun is 0.0039 W/cm2. In other words, by cutting off the wavelength at 1900nm, which targets only the unusable IR in the solar spectrum, we will reduce the heat generation in the solar cell by about 4%. 12 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

1

Top Cell

Norm Parameters

Middle Cell

0.8

B ottom Cell Normalized Low AOD AM1.5D Spectrum

0.6

Cut Off

0.4 0.2 0 300

500

700

900 1100 1300 1500 1700 1900 2100 2300 2500 Wavelength (nm)

Fig. 8: Spectral response of top, middle and bottom subcells together with the standard AM1.5G terrestrial spectrum as proposed by the National Renewable Energy Laboratory (NREL.) Marker shown is at 1900 nm.

We now go back to the 3-dimensional finite element model and calculate what that means to the cell temperature (assuming everything else being the same). The data is shown in Table 3, which is expressed as the drop in temperature (relative to the case with no IR filtering). Table 3: Reduction in cell operating temperature due to cutting off wavelength above 1900 nm Drop in Temperature (deg. C) Cell Size 1000 Suns 3000 Suns 5000 Suns 0.1cm x 0.1 cm 0.2 0.6 1.2 0.2cm x 0.2 cm 0.6 1.7 3.5 0.3cm x 0.3cm 1.01 2.9 5.8 Further efforts can be made to cut off some of the usable portion of the IR below 1900 nm. In fact, this can be done without degrading the performance of the triple-junction cell because the Ge subcell in the current triple-junction cell stack produces excess current above what the top and middle subcells are producing. Accordingly, the Ge subcell spectral response could be reduced by about 25% with minimal impact to cell performance. This corresponds to cutoff of 13 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

wavelengths above 1310 nm. By doing so, we can reduce the amount of heat generation in the solar cell by about 12%. We now go back to the 3-dimensional finite element model and calculate the reduction in cell operating temperature. The results are summarized in Table 4. In this table, we assume that the cell conversion efficiency remains unchanged at 35%. Table 4: Reduction in cell operating temperature due to cutting off wavelength above 1310 nm Drop in Temperature (deg. C) Cell Size 1000 Suns 3000 Suns 5000 Suns 0.1cm x 0.1 cm 0.6 1.7 3.5 0.2cm x 0.2 cm 1.8 5.2 10.5 0.3cm x 0.3cm 3.0 8.6 17.4 Any further reduction in IR will impact the cell efficiency. The concern with this is that it could lead to starvation of IR light in the Ge subcell, and would not produce the current needed for optimum triple-junction solar cell operation.

14 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

3.0

Performance Optimization of Dual-Junction Solar Cells

The difference between today’s triple-junction and dual-junction solar cells is that the latter has no active Ge subcell. In other words, we have more leverage of reducing the cell operating temperature by cutting off more of the wavelength without impacting the cell conversion efficiency. The drawback is obvious: dualjunction solar cells have lower conversion efficiency. For the dual-junction cell, the energy of the spectrum that is absorbed by the top and middle subcells is between 350 and 880 nm. Since there is no absorption and therefore contribution to current generation above 900 nm, this portion of the IR can be cut off or filtered with no effect on solar cell performance, as shown in Fig. 9. The irradiance of this portion of the unusable spectrum is calculated as 0.0286 W/cm2 for 1 sun. In other words, we can reduce the thermal energy absorbed in the solar cell by about 29% if we cutoff absorption of wavelength above 900 nm.

Norm Parameters

1

Top Cell

Cut Off

Middle Cell

0.8

Normalized Low AOD AM1.5D Spectrum

0.6 0.4 0.2 0 300

500

700

900 1100 1300 1500 1700 1900 2100 2300 2500 Wavelength (nm)

Fig. 9: Spectral response of top and middle subcells together with the standard AM1.5G terrestrial spectrum as proposed by the National Renewable Energy Laboratory (NREL.)

The 3-dimensinal finite element model is then used to project the dual-junction cell operating temperature, with- and without filtering. The results are shown in Fig. 10.

15 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

Cell Temperature above ambient (deg. C)

180 0.1cmx0.1cm cell, no filtering 0.2cmx0.2cm cell, no filtering 0.3cmx0.3cm cell, no filtering 0.1cmx0.1cm cell, with filtering 0.2cmx0.2cm cell, with filtering 0.3cmx0.3cm cell, with filtering

160 140 120 100 80 60 40 20 0 0

2000

4000

6000

Concentration

Fig. 10: Projected dual-junction cell temperature without- and with filtering of the spectrum

3.1

Thermal Effects on the Maximum Power

The thermal effects for dual-junction cells are equivalent to that of triple-junction cells. Dual-junction cells Vmp is approximately 0.3V less than that of triplejunction cells. Table 5 is a repeat of Table 2 with the assumption that all voltages decrease by 0.3 V and are independent of the concentration level. Table 5: The effect of temperature on Vmp and power at 1000 suns. Imp = 0.516A for 0.2cm x 0.2cm and Imp = 0.121A for 0.1cm x 0.1 cm Parameter Operating Temperature (oC) 25 45 65 85 Vmp (V) 2.38 2.29 2.20 2.11 Pmp (W) 0.29 0.28 0.27 0.26 0.1cm x 0.1 cm DJ cell Pmp (W) 1.23 1.18 1.14 1.09 0.2cm x 0.2cm DJ cell

16 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

3.2 Wafer Power Output We follow a similar exercise to the one we did for the triple-junction cell at 5000 suns. Standard Test Condition Power of 0.1cm x 0.1cm cell = (Imp = 0.52A) x (Vmp = 2.38V) = 1.24 Watts/cell Power of a whole wafer = 1.24 (W/cell) x 6,219 (cells/wafer) = 7.70 kW/wafer Power of 0.2cm x 0.2cm cell = (Imp = 2.22A) x (Vmp = 2.38V) = 5.28 Watts/cell Power of a whole wafer = 5.28 (W/cell) x 1,613 (cells/wafer) = 8.52 kW/wafer This clearly favors the use of the larger cell (the 0.2cm x 0.2cm) over the smaller cell (the 0.1cm x 0.1cm). Real Temperature Test Condition Power of 0.1cm x 0.1cm cell = (Imp = 0.52A) x (Vmp = 2.29V) = 1.19 Watts/cell Power of a whole wafer = 1.19 (W/cell) x 6,219 (cells/wafer) = 7.40 kW/wafer Power of 0.2cm x 0.2cm cell = (Imp = 2.22A) x (Vmp = 2.02V) = 4.48 Watts/cell Power of a whole wafer = 4.48 (W/cell) x 1,613 (cells/wafer) = 7.23 kW/wafer This suggests that the smaller cell is better due to the higher temperature operation of the larger cell. If, however, we filter the wavelength to bring the cell temperature down, we obtain: Power of 0.2cm x 0.2cm cell = (Imp = 2.22A) x (Vmp = 2.11V) = 4.68 Watts/cell Power of a whole wafer = 4.68 (W/cell) x 1,613 (cells/wafer) = 7.55 kW/wafer In other words, the larger cells become slightly more favorable or just about equal to the smaller cell.

17 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

4.0

Product & Process Improvements

The previous sections focused on performance optimization of existing cell technologies, taking into account the impact of filtering of the unused portions of the solar spectrum to lower the cell operating temperature. In this section, we discuss the development efforts that need to be undertaken in order to ensure a reliable operation of MJ cells in ultra-high concentration modules and to achieve lower $/Watt. 4.1 Tunnel Junction Improvements It was already mentioned in the previous section that existing tunnel junctions were not designed to handle the current densities associated with ultra-high concentration regimes. Rather, they were designed to handle concentration under 1000 suns, although they may be able to perform at concentration levels up to 2000 suns. The pursuit of tunnel junctions to operate in ultra-high concentration regimes is one development effort that needs to be pursued. This will include study of widebandgap tunnel junctions, such as AlGa(In)As/ GaInP, AlGa(In)As/ AlGaInP, AlGa(In)As/ AlGa(In)As, AlGa(In)As/ Ga(In)As, Ga(In)As/ Ga(In)As, etc., to determine improved doping methods in these materials, achieve the highest practical peak tunneling currents, and the lowest voltage drop across the tunnel junction at the incident light concentration of interest, while maximizing transparency of the tunnel junction through the use of wide-bandgap materials and reducing layer thickness. 4.2 Pursuit of Higher Cell Efficiencies In the calculation of cell output power, we assumed a triple-junction cell efficiency of 35% and a dual-junction cell efficiency of 31%. Higher cell efficiencies of 4045% are possible and they can be pursued if sufficient funding is available. Spectrolab proposes to accelerate its research into high-efficiency multi-junction solar cells for use in terrestrial concentration systems, to push the cell efficiency up to a target efficiency of 45% under the terrestrial solar spectrum at concentration. As high as present-day triple-junction cell efficiencies are, the tremendously leveraging effects of high efficiency to reduce the concentrating optics and balance-of-system costs make it highly desirable to push the efficiency as close to theoretical limits as possible. There are 2-approaches that we plan to pursue to reach a 45% efficiency goal: (i) metamorphic solar cell structures, and (ii) solar cells with 4, 5, or 6 junctions.

18 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

4.2.1 Metamorphic Solar Cells Lattice-matched (LM) Ga0.5In0.5P/GaInAs/Ge 3-junction (3J) solar cells are the highest-efficiency photovoltaic cells yet demonstrated for terrestrial concentrators, as well as for space power systems. However, the GaInP/GaInAs bandgap combination is still far from optimum for the AM1.5D terrestrial spectrum, and even higher efficiencies are possible by increasing the indium composition of the GaInP and GaInAs subcells. This lowers the bandgap of each material, thereby tuning the resulting spectral responses of the GaInP and GaInAs subcells for more efficient conversion of the solar spectrum. The higher indium composition results in a larger lattice constant than the Ge substrate, so that the GaInP and GaInAs subcells are lattice-mismatched to the Ge substrate. The lattice mismatch can produce threading dislocations in the crystal lattice, but the dislocations can be largely accommodated in a graded buffer region, so that the active cell regions have relatively low dislocation density. Such devices, in which a new lattice constant is established at which device layers can be grown relaxed and with a minimum of dislocations, are termed metamorphic (MM) devices. The ideal efficiency of 3J MM solar cells is shown as a function of the middle cell bandgap in Fig. 11, for the AM1.5 Direct, low-AOD standard spectrum for terrestrial concentrator cells adopted by the National Renewable Energy Laboratory (NREL), at 1 sun and at 500 suns. The theoretical efficiency for these 3J cells limited by radiative recombination is well over 50% at 500 suns, so that even with grid shadowing and resistive losses, efficiencies above 45% can be achieved. 110

1.305

55

1.414 eV

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AM0 AM1.5 Direct, low-AOD Ideal Eff., AM1.5D low-AOD, 1 sun Ideal Eff., AM1.5D low-AOD, 500 suns Voc X 10, AM1.5D low-AOD, 1 sun Voc X 10, AM1.5D low-AOD, 500 suns

20 10 0 0.6

0.8 1 1.2 1.4 1.6 1.8 Photon Energy Corresponding to Middle Cell Bandgap (eV)

10

Ideal Efficiency (%) and 10X Voc (V) of 3J Cell Limited by Radiative Recomb.

Integrated Current Density in Spectrum (mA/cm2)

100

5 0 2

Fig. 11: Efficiency of a Metamorphic triple junction cell as a function of the middle cell bandgap for space and terrestrial spectrum

19 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

4.2.2 Solar Cells with 4, 5, and 6 Junctions Solar cells with 4, 5, and 6 junctions are designed to divide the solar spectrum in a more advantageous partition than the conventional 3-junction GaInP/GaInAs/Ge solar cells, fundamentally increasing the energy conversion efficiency. The finer division of the solar spectrum by these cells permits three fundamental improvements in the conversion efficiency. First, fewer photons are absorbed in subcells with a bandgap much smaller than the photon energy, reducing energy losses as photogenerated carriers thermalize down to the conduction and valence band edges. Second, the lower current density of each subcell allows a ~1.1 eV GaInNAs subcell to be used, thus making use of the excess photogenerated current density in the Ge subcell for conventional 3junction cells. Third, the lower current density reduces the total resistive losses in the cell by more than a factor of two. The low-current operation of 5- and 6junction solar cells is an important advantage for reducing resistive power loss in concentrator solar cells. Figure 12 shows the cross sections of baseline 5- and 6-junction cells. The baseline 5-junction design has a bandgap combination of 2.00/1.70/1.41/1.10/0.67 eV while the 6-junction design has a bandgap combination of 2.00/1.80/1.60/1.41/1.10/0.67 eV. While the two designs share many similarities, the key difference occurs in the “splitting” of the 1.7 eV subcell of the 5-junction design into two subcells with 1.8 eV and 1.6 eV bandgaps for the 6-junction design. contact AR

AR cap contact AR

AR cap

(Al)GaInP Cell 1

(Al)GaInP Cell 1

2.0 eV

wide-Eg tunnel junction

2.0 eV

wide-Eg tunnel junction

GaInP Cell 2 (low Eg) 1.8 eV wide-Eg tunnel junction

AlGa(In)As Cell 2 1.7 eV

AlGa(In)As Cell 3 1.6 eV

wide-Eg tunnel junction

wide-Eg tunnel junction

Ga(In)As Cell 3 1.41 eV

Ga(In)As Cell 4 1.41 eV

tunnel junction

tunnel junction

GaInNAs Cell 4 1.1 eV

GaInNAs Cell 5 1.1 eV

tunnel junction

tunnel junction

Ga(In)As buffer

Ga(In)As buffer

nucleation

Ge Cell 5 and substrate 0.67 eV back contact

5-junction

nucleation

Ge Cell 6 and substrate 0.67 eV back contact

6-junction

Fig. 12: Cross-Section of a 5- and 6-junction solar cell

20 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

The bandgaps of the component subcells in a 6-junction cell along with plots of the available current density in the AM0 (space), AM1.5G (terrestrial one-sun), and AM1.5 Direct, low-AOD (terrestrial concentrator) solar spectra as a function of wavelength are illustrated in Fig. 13. The area under the spectrum curve in a specific wavelength range gives the maximum current density of a subcell for that span of wavelengths. The areas delineated by the subcell bandgaps are comparable in size, allowing series-interconnected subcells to be current matched. Theoretical efficiencies for this type of cell at 500 suns exceed 50%, and practical solar cells are expected to be able to reach over 45% for terrestrial concentrators. 2.0 1.8 1.6 1.41 eV

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Fig. 13: Division of standard solar spectra by the bandgaps of the 6 subcells in a 6junction cell.

4.3 Scribe & Break Process Development The ultra-high concentration modules require that the solar cell size be kept as small as 0.2cm x 0.2cm or less, as we have seen from the temperature projections with- and without IR filtering. In doing so, the number of cells out of a single wafer is in the order of thousands, with the number of cuts needed to separate the solar cells being a major cost driver if we continue to use traditional cutting methods; namely, saw dicing. Rather, we must pursue alternative cutting 21 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

methods similar to those used in the microelectronics industry, i.e., scribe-andbreak. Previous preliminary studies have shown that to accomplish scribe-and-break successfully, the front and back metal thicknesses need be substantially reduced. Typical bus bar, gridline and back metal thicknesses are several microns in height. It has been recommended that the metal thickness layers should be about several thousand Angstroms for the scribe-and-break process. This will have an impact on the gridline optimization process we discussed previously. Figure 14 shows an example of the relative power loss at 5000 suns when the metal thickness layer is reduced from 5 µm to 5000 Å. The increased loss from the difference in metal layer height is only 1.9%--an acceptable loss. 100 5000 SUNS MODEL

Fractional Power Loss (%)

Metal Thickness = 5 microns

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Fig. 14: The effects of the front contact metal thickness on the fractional power loss of concentrator solar cells.

Once a scribe-and-break process is developed and qualified for the small concentrator cells, we will need to develop processes for wafer level test and pick-and-place for the cells. These activities are critical to reducing the cell fabrication cost and ensuring a competitive $/Watt. 4.4

Reducing the Ge Wafer Cost

Concentrator solar cells are grown on Ge wafers. The Ge wafers represent roughly about 25-30% of the solar cell cost. So far, most of concentrator solar 22 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

cells are built on high-quality (i.e., low defect counts) Ge wafers. The choice of low-cost Ge wafers may lead to lower cell fabrication costs without impacting the cell quality. This effort will entail purchase of several batches of low-cost Ge wafers with different defect levels, growing epitaxial structures on these wafers and fabricating and testing them into concentrator cells. By associating the performance and reliability of the different cells to the different wafers, we should be able to set acceptable specs for terrestrial wafers. Another radical way of reducing the cost of cell fabrication is to develop a process to remove the epitaxial layer grown on top of the Ge wafer, and then reuse the wafer for another growth run. This is a process that is at its infancy; hence, it will require major development to bring down to reality. However, if successful, it may have serious consequences on reducing the costs of MJ solar cells. In this regard, scientists just developed an ultra-thin 2J GaInP/GaAs space solar cell with 25% efficiency. The procedure involves the growth of GaInP and GaInAs epitaxial layers on a substrate, perhaps Ge. Then the epilayers are lifted off and transferred to a metal film where the film now acts as the substrate. The top GaInP subcell is quite thin. The disadvantage of this process, however, is that to make the GaAs layer as thin as possible to increase flexibility, the GaAs current starts to plummet due to its thin layer. Current generation is proportional to light absorption. The thicker the layer, the more light is absorbed, and the higher the current. Although the layers are thin, this appears to be a minor setback as the metal substrate serves to reflect light back into the junctions of the GaInP and GaAs layers. This produces more photo-generated carriers, i.e. electrons (and holes) that contribute to the generation of current. Reports are based on a 4cm x 7cm GaInP/GaAs dual-junction cell that corresponds to total layer thicknesses between and 1 and 2 µm (Ge wafer thickness is 0.007 inches).

23 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

5.0 Concentrator Cells Cost Projections We now turn our attention to the economics equation for ultra-high concentrator cells in sizes of 0.1cm x 0.1cm and 0.2cm x 0.2cm. The cell cost is expressed in terms of $/Watt. Keep in mind that in this chart, the Watts are calculated at 25 deg. C operation (standard test conditions). Figure 15 shows the projected cell cost for today’s triple-junction cells, while Fig. 16 shows the projected cost for a 45% cell. $0.30

Cell Price ($/Watt)

$0.25 $0.20

1000 suns 3000 suns

$0.15

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Total cell area (cm^2)

Fig. 15: Projected Cell Cost (for today’s triple-junction cells) $0.25

Cell Price ($/Watt)

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$0.15

3000 suns 5000 suns

$0.10 $0.05 $0.00 1,000

10,000

100,000

1,000,000 10,000,000

Total cell area (cm^2)

Fig. 16: Projected Cell Cost (for 45% cell)

24 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

In both graphs, the cell output is calculated at 25 deg. C (standard test condition). Further, different cost reduction activities have been assumed in the generation of these charts (when the volume approaches 1,000,000 cm2), including implementation of scribe-and-break, automated wafer level test. Also, a gradual reduction in the Ge wafer cost has been assumed. From this data, it is clear that there is a real need to increase the concentration level to 3000 suns (big reduction in cost between the 1000 suns case and the 3000 suns case).

25 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.

6.0

Summary & Conclusions

The operation of MJ cells in concentration regimes of 1000-5000 suns will require that the cells be kept smaller than 0.2cm x 0.2cm in size. This will allow direct bonding of the cells to heat spreaders, which will provide for efficient heat dissipation using passive cooling even under concentration of 1000-5000 suns. We analyzed the impact of filtering the unused portion of the infrared radiation to reduce the cell temperature. It seems that there is benefit in cutting off wavelength above 1310 nm for 0.2cm x 0.2cm cells (10 deg C drop in temperature at 5000 suns), which will have minimal impact on cell performance. The benefit was much smaller for the 0.1cm x 0.1cm cells, with temperature reduction under 5 deg. C. However, in dual-junction cells, where the cutoff wavelength could be as low as 900 nm, the benefit of IR filtering was much more pronounced. There are modifications to the MJ cells that will need to take place to enable the cells to operate reliably under ultra-high concentration levels. They include modifications to the existing tunnel junction structures since current tunnel junction structures cannot operate reliably above 1000-2000 suns. They also include modifications to the metallization schemes to reduce series and contact resistance and make the MJ cells work efficiently and reliably in ultra-high concentration modules. In terms of cost reduction, the fact that the cells are going to be under 0.2cm x 0.2cm in size will require changes to the existing processes from saw dicing to scribe-and-break methods. Further cost reduction activities will need to focus on the qualification of lower cost, terrestrial-grade Ge wafers and on the implementation of automated test methods (enabling tests of the cells on a wafer level). By applying all the above improvements, the solar cell cost could be as low as $0.05 per Watt or even lower at concentration levels above 3000 suns. Further cost reduction could be driven by developing concentrator cells with 45% conversion efficiency. Although efforts to achieve 45% cell efficiency require substantial funding, increasing cell efficiency is very leveraging not just in bringing down the cell cost but also in bringing down the entire system cost.

26 The data in this report are controlled by the terms of the Non-Disclosure Agreement between Mok Industries & Spectrolab, and by the Terms and Conditions of Sale for Spectrolab Sales order # 5926.