Open-Circuit Voltage for Illuminated Electrodes

What happens when the illuminated electrode is at open circuit? The answer to this question is perhaps most easily seen from Equation 15.21 for an n-type semiconductor, which includes both the photocurrent and the current due to the potential-dependent majority carrier current. At open circuit, the net current is equal to zero. In an n-type semiconductor, this happens when the negative charge in the bulk semiconductor (away from the interface) builds up due to electron–hole separation to the extent that the back flow of electrons toward the interface is equal to the anodic photocurrent due to holes. Under these conditions, Equation 15.21 can be solved for the open-circuit voltage of an n-type semiconductor to yield

(15.25)
VOC is the open-circuit voltage and U is the equilibrium voltage in the dark, which is determined by the equilibrium potential of the redox couple in solution for the simplifying assumptions that we have made. The open-circuit voltage is the maximum voltage (magnitude) that can be obtained from a solar cell. Its value depends on the intensity of the incident light and on the saturation current density, . Consequently, the absolute value of VOC increases with increasing light intensity and with decreasing saturation current. Note that VOC is lower (i.e., more negative) than the equilibrium voltage for n-type semiconductors.

ILLUSTRATION 15.6
For the n-type semiconductor from Illustration 15.4, calculate the open-circuit voltage (net current = 0), when the photocurrent is 25 mA·cm−2.

SOLUTION:
The photocurrent for an n-type semiconductor, due to separation of electron–hole pairs at the semiconductor–electrolyte interface, is positive or anodic. From Equation 15.25, at open circuit with the parameter values from Illustration 15.4,

Therefore, .

is the overpotential at which the magnitude of the “dark current” (cathodic) equals that of the anodic photocurrent. The photocurrent is independent of the overpotential as long as there is a field of sufficient magnitude to separate the electron–hole pairs generated by light absorption. As shown in Figure 15.19, the photocurrent is the dominant current at reverse bias conditions.