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60%

A~

3

>100

R dominance

50

100

Z_ . . ,0

0•

1..

200 300 V (mV)

400

500

0

10

20

... 30 40 I (mA)

.L___••_ 50

60

Fig. 1. The dark I-V response of photovoltaic devices based on p+/n porous jic-Si films with (A) 20%, (B) 40%, and (C) 60% porosity. The influence of the series

Fig.2. Plot of the deviation of the voltage from the ideal behavior (zero series resistance) vs. current. The slope of the curve gives series resistance. Ideal diode behavior (AV=0) is

V>300 mV.

film is 40% porous.

resistance results in nonideal behavior for

observed at low injection levels. The PMSi

Under illumination, an ideal solar cell is equivalent to a constant current generator in parallel to a p-n junction diode. Inc luding the R, element, the current-voltage relationship is as follows:14 IL:= IR- Io [exp(q/mkT (VL + IL Rs))]

(3)

where IL is the load current, and IR is the photocurrent (short-circuit current). Figure 3 shows the fourth quadrant response of the three devices under simulated AM1 illumination. The values of Voc are 0.57 V, 0.55 V, and 0.5 V and those of Isc are 40 mA, 50 mA, and 20 mA for devices A, B, and C, respectively. The voltage and current corresponding to the maximum power points were determined by applying constant power contours to Fig. 5. Their values are found to be{Vm, Im} = {0.4 V, 28 mA} for device A; {0.37 V, 39 mA} for device B; and {0.2 V, 13 mA} for device C. Again, the I-V response of the control device was similar to device A, with a slightly smaller Ise value (37 mA). Using (3), R, can be determined independently by the variable illumination intensity technique proposed by Wolf and Rauschenbach :15 Rs = (VLI

627

- VL2)/(IL2 - ILl)

(4)

where VL1, VL2 (ILI, IL2) are the load voltage (current) under two different intensities, such that (IRI - ILl) = (IR2 - IL2); i.e. the diode currents are the same in both cases. In Figure 4, we have plotted the I-V response of device B at 100% and 50% intensities. The difference in Voc is negligible, while Isc drops from 50 mA to 28 mA. To calculate R,, we chose VL1 = Vm, and ILI = Im.The value of Rs is then found to be [(490-370)/(39-17)] = 5.4 Q for device B. Similarly, R, is determined to be 2.8 L (control device), 3.1 L (

=20%), and 4 L (

=30%). The agreement with the values of R, determined earlier validates our analysis of the dark I-V response. The same technique could not be applied for high porosity film (P=50%, 60%) based devices, because of the high series resistance. 600 500

500

400

400

300

2 300

200

200

100

100

L2

IL2

14

0

_

R12R

E1

0

5

10 15 20 25 Current density (mA/cm 2)

30

0

I_

0

10

20

30 40 I (mA)

50

60

Fig. 4. The I-V response (fourth quadrant) of device B (

=40%) under (a) 100% and (b) 50% intense AMI illumination for the determination of series resistance. The data points chosen (a) (0.37 V, 39 mA), and (b) (0.49 V, 17 mA), are such that the diode current is the same for the two cases.

Fig. 3. The I-V response (fourth quadrant) of devices (A) (

=20%), (B) (

=40%), and (C) (

=60%)