@Devin-M, let me point out something else that you may be running into besides measurement errors and non-deal aspects of circuit setups.
The emf point at which a photodetector exhibits zero [dark] current is not necessarily at exactly 0 Volts. It's highly dependent upon the circuit in which it is placed. This is due to the fact that photodetectors are non-linear devices and have
junction emfs. The P-doped and N-doped material in the photodetectors act as dissimilar metals (or in this case, dissimilar semiconductors) and a residual emf maybe present across its terminals, even though no current flows.
Certainly, if the photodetector is by itself, not connected to anything, this emf will exist. It can also exist if placed in a circuit, particularly when other non-linear devices, such as a diode, are wired in parallel.
As an analogy, this is similar to how you wire two batteries in parallel, and no current will flow between them. Don't take this analogy too far though -- batteries have significant energy stored within them, but diodes do not. (And photodetectors do not contain significant stored energy when they and their sourroundings are all at the same temperature.)
So the idea that the voltage across the terminals of a photodetector is not precisely 0 when the minimum current point is reached, should not come as a complete surprise. Again though, it all depends on the circuit details.
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But let me repeat my main point again. If you place a photodetector in a
passive circuit, and the photodetector, the other circuit components, and the surroundings are all at the same temperature (that also means no external light sources -- only the thermal background within the dark enclosure),
the current through the photodetector will be zero. A this point, the voltage across the terminals of the photodetector might not be exactly 0, but I can guarantee you that the steady-state, DC current through the photodetector
will be 0.