This method consists of monitoring applied voltage across the cell as a function of time that is necessary to maintain a constant current through the solar cell after the current is changed stepwise, e. g., from zero to a predetermined fixed value (Boer 1981a, 1981b, 1981c). When the current is increased, the space charge is increased, caused by depletion of donors or traps that turn positive (Fig. 33.11a). Conversely, a decrease of the current causes a filling of such centers, neutralizing them and reducing the slope of the characteristic, i. e., causing the voltage drop to decrease (Fig. 33.11b).
If, however, the forced increase in current causes a depletion of acceptors or acceptor-like deep hole traps, e. g., caused by Frenkel-Poole excitation by field quenching causes a reduction in space charge by compensation and thereby an increase in the slope of the characteristics, the opposite behavior as found for depletion of donors.
The changing space charge in part of the barrier is illustrated in Fig. 33.12. In panel a we show a slow depletion of a deep electron trap with higher applied voltage, causing a reduction of the voltage drop (area under the F(x)–curve) as a layer with increased space charge becomes established.
This results in a higher field slope near the interface that can reach the same Fj, thereby maintaining the same current.
When the critical field for field quenching is reached at the interface, the space charge-free field-quenched region with constant critical field Fc expands as shown in Fig. 33.12b. An intermittent region is created with a high field slope where deep electron traps are depleted before quenching starts.
Figure 33.13 shows corresponding experimental results. Three characteristics are given schematically in panel a. When the current is changed to a constant value Io, a voltage of ~0.2 V is necessary to maintain this current for curve 1; however, in time
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Fig. 33.12 Field distribution kinetics in a barrier layer (a) with gradual depletion of a deep trap; (b) with depletion of a deep trap, but at a field at which field quenching starts to reduce the space charge near the interlayer and therefore limits the field |
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Fig. 33.13 Kinetics of the current-voltage characteristics within the DRO-range. (a) Schematics of three non-stationary characteristics; when constant current I0 is maintained, the applied voltage changes in time as the characteristic develops from curve 1 through curve 2 to curve 3. (b) Voltage drop as a function of time after the current is changed from zero at Voc for 2 min. to I0 = —530, —600, —650, —700, and —820 mA for curves 1-5, respectively (after Boer 1981a, 1981b, 1981c) |
the applied voltage needs to be reduced, reaching a minimum at —0.15 (curve 2), and then increased again to —0.05 V (curve 3) to maintain I0.
The actual voltage kinetics is shown in Fig. 33.13b for a Cu2S/CdS cell that shows JV-characteristics with hysteresis similar to the one given in Fig. 33.10. The observed kinetics depends on the degree of preceding trap filling (waiting at a certain point of the characteristic), on the value of I0, and on the temperature.
In curves 8 and 7 of Fig. 33.13b, one can discern the three voltage drop ranges shown in panel a. First a shift toward higher negative voltage, indicating trap depletion; this shift is very fast, and barely resolved near t = 0 for curve 7. This range overlaps with the voltage decrease caused by the start of field quenching that be-
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Fig. 33.14 Voltage drop across a Cu2S/CdS solar cell similar to the one used in Fig. 33.13 after switching from I = 0 to 860 mA at the temperatures listed in the three panels and after waiting at Voc for the time indicated at each curve. (b) Logarithm of the half-time of the voltage decrease taken from subfigures. (a) Curves of 1 min. rest at Voc are used (after Boer 1981a, 1981b, 1981c) |
comes dominant near 10 s. It is then followed by a slow rise beyond 40 s; this rise is probably due to an even slower release of electrons from deeper electron traps, thereby lowering the compensation.
When waiting at Voc for different lengths of time (shown as family parameter in Fig. 33.13) and then plotting the time to achieve half of the quenching obtained from the abscissa for different temperatures in a semi-logarithmic plot versus 1/T (Fig. 33.14b) one obtains an apparent activation energy of ~0.5 eV for the filling of deep traps that makes it more time consuming for quenching, the more of these traps are filled.
The examples are given here to illustrate the sensitivity of an incompletely filled out current-voltage characteristic to trap kinetics. Any characteristic that has a substantial square-root range (indicating a DRO-range) between the Boltzmann and the current saturation range offers an opportunity to study such kinetics. For example, in this DRO-range, the current-voltage characteristic relates as a simple drift
2p(Voc V)
Jn = e^nHjFj with Fj = , (33.14)
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which yields for the voltage drop across the solar cell for trap filling with p = e[Nd – nd(t)]:
jn2
(e^nnj)2[Nd – nd(t)]
