## The Prototype

We have built and tested a Microconcentrator system with Sphelar® discrete photovoltaic cells from Kyosemi Corporation and achieved roughly 10% system efficiency (Figure 1). This was done using arrays of spherical silicon photovoltaic cells with elastic mirror contacts behind an acrylic lens-mirror. Individual Kyosemi spherical Sphelar® cells in this array are shown in Figure 2.

Figure 1: Prototype Micro-concentrating cylindrical acrylic lens-mirror optics and 495 spherical bead Sphelar® photovoltaic cells. In this photo part of the frame has been removed to reveal the side of the array. Each lens is 5 mm wide and 75 mm long. The lens-mirror is 75 mm X 75 mm.

Figure 2: 1.8 mm diameter scanned image of two Kyosemi Sphelar® solar cells.

Figure 3: Backside view of the array module. Note: the back plate forms heat sinking fins.

## Single Strip Array Results 2007

We assembled and tested a prototype strip of cells in a mirrored contact. The following data were taken before the cell-mirror-contact assemblies were glued to the optical lens covers. This sample test had 31 Kyosemi 1.2 mm diameter Sphelar® beads in a trough mirror contact before it was incorporated into the 495 cell array. The distance between each lens in the concentrating optics is 5 mm. The following data show the power vs. voltage curve of the array. The assembly achieved solar conversion efficiency of roughly 9.1 % and an effective utilization of the beads of 4.8 times over the single beads without light concentration.

## Calculated Performance

*Peak power output:* 15 milliwatts

*Maximum width of cylindrical input lens:* 5 mm

*Diameter of Sphelar® photodiode bead:* 1.2 mm

*Effective input area of lens:* 1.2 mm X 5mm X 31 = 186 mm2 or 1.86 cm2

*Solar irradiance of 0.97 of AM1 sun 3:23 pm March 26, 2007 Los Alamos:* 0.97X 925 Watts/m2= 897 W/m2 or 0.0897 W/cm2

*Estimated efficiency:* 0.015 W/(0.089 W/cm2*1.86cm2)=0.0906 or 9.1%

The 1.2 mm Sphelar® photodiode beads have a power output of 0.1 milliwatts under AM1 direct illumination.

** Estimated effective concentration factor: **15mW/(31*0.1mW) = 4.8

The array has an angular full-width-half-peak response of 5 degrees perpendicular to the trough axis and 35 degrees in the trough axis. This is approaching what is desirable for a single axis tracked array.

**Estimated peak power output of prototype 495-cell array: **0.25 Watts.

### Utilization of silicon in the prototype is the 0.25 Watts/gm of silicon.

Utilization of silicon in a conventional 300-micron thick silicon photovoltaic cell with 10 % efficiency is 0.137 Watts/gm of silicon. (Both are crystalline silicon cells so the same efficiency is assumed to make a simple comparison)

**Ratio of Silicon Utilization of prototype to conventional cell: **1.8:1

If we are compared to a high performance conventional crystalline silicon cell 150 microns thick and 20% efficiency then the **ratio of silicon utilization of the prototype to the conventional cell is:** 0.8:1

The prototype increases utilization of silicon over conventional planar crystalline silicon cells. Further improvements proportional to the sphere diameter are expected as the diameter of the silicon spheres is reduced. Efficiencies as high as 19.7% have been obtained from the Sphelar® cells. Cost reductions can be realized by reducing the amount of silicon per watt achieved with spherical geometry, but also because the bead formation is more efficient than forming ingots and sawing (~50% kerf losses and unused silicon). There is relatively little wasted silicon in the formation of the free-fall formed spheres. Thus a rough factor of 2X improvement in utilization can be realized.

The silicon feed stock for spheres is expected to be lower purity; $40/kg to 60/kg (because of the migration of impurities to the outside of the sphere in free fall crystallization), rather than high purity; $200/kg silicon. Thus, a factor of roughly 4X reduced cost due to the silicon feed stock can be realized.

The overall effective cost reduction for material cost of silicon per unit mass is 1/(1.8*2*4)=0.068 or 6.8% of the cost of conventional crystalline photovoltaic cells. To translate this to material cost of cells:

### Cost of silicon per unit mass used/Silicon utilization of watts per unit mass=Cost per Watt:

**This Prototype: ***$50/kg/(1000*0.25 Watts/gm) =$0.20/Watt
**Conventional Cell: **$200/kg*2 /(1000*.137 Watts/gm) = $2.92/Watt

**The material cost reduction mechanism necessary for photovoltaic cells to be competitive with conventional power sources has been demonstrated in this prototype. **

Measurements of conversion efficiency of Sphelar® cells have obtained efficiencies over 19% at one sun (AM1). If we reduce the losses in the concentrating optics and increase the light intensity on the cells we are expecting to achieve 20% system efficiency from arrays. If we also combine this with 50% less material used if we reduce the diameter of the Sphelar® cells to 0.6 mm: Silicon utilization scaling: Area/Volume=1.2/0.6=2. Then the future array cost per Watt can be projected to be roughly four times better then our experimental results.

$50/kg/(1000*(.2/.093)*(1.2/0.6)*(0.*0.25 Watts/gm) =$0.047/Watt

If we compare this to roughly the best performance we expect from a crystalline conventional silicon solar cells with 20% efficiency and thin wafers of 150 microns,

$200/kg*2 /(1000*(.2/.1)*(300/150)*2.137 Watts/gm) = $0.73/Watt

**We can expect to achieve 6.4% the price of the conventional crystalline silicon solar cell with 4.8 X Micro concentration optics and 50% smaller Sphelar®? cells. A savings of 93.6%!**

### Effect of increasing concentration for solar tracking power arrays

From our measurement data on 1-2 mm square silicon cell coupled with focused light from 14 mm diameter aperture spherical optic, a 28 X light concentration was achieved while still efficiently removing the heat. This 28X concentration is our target concentration for two axis-tracked eQarraysTM. The utilization of the semiconductor increased by the ratios of concentration from 4.8 X to 28 X. or a ratio of 28/4.8=5.8, Thus, the cost of the silicon with 0.6 mm Sphelar® cells to the arrays then reduces to:

$50/kg/(1000*(.2/.093)*(1.2/0.6)*(28/4.8)*(0.*0.25 Watts/gm) =$0.008/Watt

**From this estimate we have shown how the cost of the semiconductor can be reduced to roughly 1% of the cost of the conventional crystalline silicon photovoltaic arrays using microconcentration and Sphelar® cells. **