#### LESSONS OF EASTER ISLAND

March 17th, 2016

Figure C.3 shows the quantum efficiency of a high-efficiency thin-film Si solar cell with a thickness of 46.5 pm (see description of Cell A on p. 83 for more details) under illumination with light of wavelengths 500 and 800 nm. For both wavelengths the IQE data depend on the forward bias voltage Ub. At bias voltages up to 500 mV the value of IQE{500 nm) is constant, while IQE($00 nm) starts to increases at 350 mV. For voltages Ub >550 mV IQE(500 nm) and IQE(500 nm) both decrease.

Interpretation of the measurement

Light of wavelength 500 nm penetrates a distance of 0.9 jam into the cell. Hence, the light is mainly absorbed in the emitter and the quantum efficiency therefore reflects the recombination in the emitter that is known to be, in general, independent of the injection level.

In contrast, light of wavelength 800 nm penetrates 12 jam into the cell and is mainly absorbed in the base. The quantum efficiency at 800 nm is thus dominated by recombination in the base and at the back surface. Since the diffusion length exceeds the base thickness, IQE(800 nm) actually reflects recombination at the Si/Si02 back surface, which is known to decrease with the injection level. A decreasing surface recombination increases the quantum efficiency at voltages above 350 mV.

The decrease of the differential resistance Ro{Ub) with increasing forward bias Ub causes the common decrease of IQE(500 nm) and IQE(800 nm) at voltages greater than 550 mV. This decrease is thus not due to a change in the recombination rates with the injection level [31]. The larger the Rs (see Figure C.2), the more photogenerated current is diverted through the diode, since the value of RD decreases with increasing bias voltage Ub. The circles in Figure C.3 depict the measured ratio IQE(5OOnm, Ub)/IQE(500 nm, 0). In addition, this figure also shows IQE(500nm, Ub)/IQE(500 nm, 0) as measured

Figure C.3. Internal quantum efficiency IQE(500 nm) and IQE{800 nm) measured at two wavelengths for a thin-film high-efficiency solar cell from crystalline Si. Data from Ref. [405]. |

with Rs being increased by 2.2 Q (open circles) and by 10 Q (filled triangles) with external resistors. As expected, the voltage dependence is enhanced by increasing Rs.

Ratio IQE(Ub)/IQE(0) determined from the current-voltage curve I(U)

If the reduction of the measurement signal is a purely resistive effect, it should be possible to calculate the reduction factor from the measured dark current-voltage curve I(U) of the solar cell. With increasing forward bias Ub the small signal resistance

of the diode decreases. The analysis of the equivalent circuit shown in Figure C.2 yields ^-dependent output voltage

UjUb) = Q„(Ub)RopIm

that depends on a voltage-dependent resistance factor

Using Eq. (C.2) we derive the resistance factor

directly from the measured current-voltage curve I(U) of the solar cell. Our above interpretation of the experimental data shown in Figure C.3 is equivalent to the hypothesis

IQE{500nm, Ub)

IQE(500 nm,0) (C’6′)

We test this hypothesis by comparing the quantum efficiency ratio IQE(500 nm, Ub) / IQE(500 nm, 0) and the resistance factor QR in Figure C.4. For the calculation of the resistance factor QRi we choose a value for Rs that best fits the quantum efficiency ratio /g£(500nm, Ub)/IQE(500 nm, 0). The fits are the solid line lines in Figure C.4 and are achieved for Rs = 0.16 Q, 2.0 Q, and 9.6 Q. The close agreement to the actually inserted resistor values of 0 Q, 2.2 Q, and 10 Q confirms our interpretation of the decrease of IQE(500 nm) in Figure C.3.

Correction of experimental IQE spectra for resistance factor QR

The quantum efficiency spectrum has to be corrected for this effect, which is not related to the recombination properties, by

Figure C.4. Measured quantum efficiency ratio for wavelength 500 nm (symbols). Resistance factor Qr calculated from the dark current-voltage curve for various series resistance values Rs (solid lines). Data from Ref. [405]. |

In the rest of this work only the corrected quantum efficiency IQE* is used when quantum efficiency data under bias voltage are presented. We omit the asterisk to simplify the notation. The impact of a series resistance on quantum efficiency measurements is also discussed in Refs. [406, 407, 408].

## Leave a reply