# Bifacial Solar Cells

Some of the types of solar cells that have been discussed so far can trap in principle incident light bilaterally, which opens up promising new applications in that bifacial modules need not necessarily be tilted towards the Sun but can also be oriented vertically (e. g. in a north-south direction). On the other hand, normally oriented solar generators with bifacial modules whose rear side also captures light reflected off the ground yield 10 to 15% more energy. The company Solar Wind Europe sells pilot-production bifacial modules in the 40 to 120 W power range, although the two sides of these modules do not make equally good use of incident light, i. e. the light incident on one side is used more efficiently than that incident on the other side (e. g. only about half of the light incident on the rear side is used). In addition, at Expo 2005 in Japan, Hitachi unveiled a pilot-production bifocal module. Only time will tell the extent to which such modules will be able to gain a reasonable market share and whether larger vendors will begin making such products.

3.6 Examples

Problem 1

A silicon solar cell whose cell area is AZ — 225 cm2 exhibits Voc of 600 mV, Isc of 7.5 A and Pmax of 3.4W at STC (1 kW/m2, AM1.5, 25°C).

This solar cell is now being operated in the presence of the same irradiance but at a cell temperature of TZ — 75 °C. It can be presumed that the temperature dependence of this module will be as in Figure 3.18.

(a) Voc (with Tz — 75 ° C)

(b) ISc (with Tz — 75 °C)

(c) Pmax (with Tz — 75 °C)

(d) FF (with TZ — 75 °C)

(e) zpv (with TZ — 75 °C)

Solution:

(a) Voc « (1 – 0.2)Voc(STC) « 480mV

(b) ISc ~ (1 + °.°2)ISc(STc) ~ 7.65 A

(c) Pmax « (1 – 0.235)Pmax(STc) « 2.60W

(d) FF — Pmax/(Voc ■ Isc) « 70.8%

(e) ZPV — Pmax/(Go ■ Az) ~ 11.6%

Hence, as temperature rises, Voc, Pmax and zpv, and also the fill factor FF, decrease.

Problem 2

For a currently non-realizable idealized solar cell whose diode quality factor is n — 1, which exhibits no ohmic loss, whose cell area is AZ — 100 cm2, and which in practice also reaches the theoretical limits for Jsc, Voc, FF and zt at STC (1 kW/m2, AM1.5, 25 °C), the following elements are to be determined using the relationships referred to in Section 3.4:

(a) Isc, Voc, FF, Pmaix and zt for an idealized monocrystalline silicon solar cell (EG — 1.12 eV).

(b) Isc, Voc, FF, Pmax and zt for an idealized CdTe solar cell (EG — 1.46 eV).

Solution:

(a) According to Equation 3.4, VT — 25.68 mV for n — 1 at 25 °C.

According to Figure 3.20, JSC ~ 43.1 mA/cm2 ) ISC ~ AZ■ JSCmax — 4.31 A.

Using Equation 3.22 or an approximation based on Figure 3.23, the following is obtained: VOC — 767 mV (KS — 40 000 A/cm2).

Using Equation 3.12 or an approximation based on Figure 3.24, FF,- — 0.857 is obtained.

Using Equation 3.19, the following holds true: Pmax — VOC ■ ISC ■ FF, — 2.83 W.

Using Equation 3.20, or directly based on Figure 3.25, zt — Pmax/(Go ■ AZ) — 28.3%.

(b) According to Equation 3.4, VT — 25.68 mV for n — 1 at 25 °C.

According to Figure 3.20, JSC ~ 30.1 mA/cm2 ~ ISC ~ AZ ~ JSCmax — 3.01 A.

Using Equation 3.22 or an approximation based on Figure 3.23, the following is obtained: VOC — 1.098 V (KS — 40 000 A/cm2).

Using Equation 3.12 or an approximation based on Figure 3.24, FF, — 0.891 is obtained.

Using Equation 3.19, the following holds true: Pmax — VOC ■ ISC ■ FF;- — 2.94W.

Using Equation 3.20, or directly based on Figure 3.25, zt — Pmax/(Go ■ AZ) — 29.4%.

Problem 3

For the currently non-realizable idealized solar cell as in Example 2(a) whose diode quality factor is n — 1, whose characteristics have been provisionally defined, which exhibits no ohmic loss with a cell area of AZ — 100 cm2, and that in practice likewise reaches the theoretical limits for JSC, VOC, FF and zt, using the relationships referred to in Section 3.4 calculate the theoretical efficiency ztin monochro­matic red light (l — 0.77 pm) with Go — 1 kW/m2 and cell temperature TZ — 25 °C.

Solution:

According to Equation 2.33, the energy of such a red-light photon is EPh — 2.58 ■ 10~19 J — 1.61 eV.

The number of photons per second and unit area arriving at the solar cell is as follows: nPh/(A ■ t) — Go/EPh — 3.88 ■ 1017photons/cm2s ) current density JSC — nPh ■ e/(A ■ t) — 62.1mA/cm2. Using Equation 3.22, it follows that maximum possible open-circuit voltage is VOC — 777 mV (KS — 40 000 A/cm2).

Using Equation 3.12, the idealized fill factor FF, — 0.858.

Using Equation 3.19, Pmax — FF,-■ VOC■ JSC■ AZ — 4.14W is obtained.

Using Equation 3.20, it follows that zt — (PmaJAZ)/Go — 41.4%.

Hence solar cell efficiency in monochromatic light can be considerably greater than in the AM1.5 spectrum.

Problem 4

A currently non-realizable idealized tandem solar cell whose diode quality factor is n — 1, which exhibits no ohmic loss (as in Example 2) and whose cell area is AZ — 100 cm2, is composed of two electrically isolated solar cells that are optically connected behind each other (four-terminal tandem cell). The band gap energy EG of the front and back cell is 1.75 and 1 eV respectively. Inasmuch as this idealized example presupposes that the front cell will absorb all sufficiently energized photons and that all insufficiently energized protons will be allowed through unimpeded, the possible current density (based on Figure 3.20) of the rear cell will be reduced by exactly the current density of the front cell. Based on these suppositions, the following elements are to be calculated using the relationships referred to in Section 3.4, at STC (1kW/m2, AM1.5, 25 °C):

(a) ISC, VOC, FF, P^x and zt for an idealized front solar cell (EG — 1.75 eV).

(b) ISC, VOC, FF, Pmax and zt for a rear solar cell (EG — 1 eV).

(c) Pmax and Zt for the cell as a whole, assuming that both cells of the tandem array are operated at MPP.

Solution:

(a) Front solar cell (EG —1.75 eV):

According to Equation 3.4, VT — 25.68 mV for n — 1 at 25 °C.

According to Figure 3.20, JSC — JsC-F ~ 20.7 mA/cm2 ) IsC-F ~ AZ ■ JSCmax ~ 2.07 A.

Using Equation 3.22 or an approximation based on Figure 3.23, the following is obtained: VOC — 1.378 V (KS — 40 000 A/cm2).

Using Equation 3.12 or an approximation based on Figure 3.24, FFi — 0.909.

Using Equation 3.19, the following holds true: Pmax — Pmax-F — VOC ■ Isc ■ FF; ~ 2.59 W.

Using Equation 3.20, or directly from Figure 3.25, zT — Pmax/(Go ■ AZ) — 25.9%.

(b) Rear solar cell (EG — 1 eV):

According to Equation 3.4, VT — 25.68 mV for n — 1 at 25°C.

According to Figure 3.20, with EG — 1 eV, JSC « 47.7 mA/cm2.

However, for a tandem cell, JsC-F — 20.7 mA/cm2must be subtracted from the front cell:)

JSC-R — JSC ~ JSC-F — 27.0mA/cm2 ) ISC-R ~ AZ ■ JSC-R ~ 2.70A.

Using Equation 3.22 or an approximation based on Figure 3.23, the following is obtained: VOC — 635 mV(KS — 40 000 A/cm2).

Using Equation 3.12 or an approximation based on Figure 3.24, FF; — 0.835 is obtained.

Using Equation 3.19, it then follows that:Pmax — Pmax-R — VOC ■ IsC-r ■ FF; ~ 1.43.

Using Equation 3.20 (but not directly based on Figure 3.25), zt — Pmax/(Go ■ AZ) ~ 14.3% is obtained.

Hence the back cell converts into electrical energy an additional 14.3% of total energy arriving at the solar cell. However, as the higher-energy photons have already been processed by the front cell, referred to the residual light that penetrates to the back cell, the efficiency of the back cell is considerably higher.

(c) Total for the tandem array:

Total Pmax — Pmax-F + Pmax-R — 4.02 W. Using Equation 3.20, the following is obtained:

Theoretical efficiency of the entire tandem array: zT — Pmax/(Go ■ AZ) ~ 40.2%.

Updated: August 4, 2015 — 11:11 am