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1949
LEAD-SULFIDE PHOTOCONDUCTIVE CELLS
693
We may write, for the conductance G of the area between the electrodes, or the resistance R
G = go r(X/L) (la)
and
R = P»
(Ib)
Equation (Ib) is the more familiar form of the fundamental resistance equation, but (la) and (Ib) are completely equivalent. If the specific conductance go is not constant over the whole area, it may be
shown that
G = ^r(X/L), (2)
where g0 is the average value,
l/LXffg*(XtL) dX dL,
The only assumption we shall make about the photoconductive effect is that the specific conductance go is related to light intensity / by an equation of the form
go = A + kl.
If the light intensity is not uniform over the surface, it may still be shown that
^ = A + kl,
where I is the average intensity over the
sensitive area. The constant A results from the fact that the dark
resistance of the cell is finite. Accordingly,
G = (A + kI)(rX/L). (3)
Fig. 1— Schematic representation of photoconductive surface (cross-hatched area X with electrodes a, a.
First note that the conductance does not depend upon the size of the sensitive area but only on the shape factor X/L and the thickness of the layer. Second, the response depends upon the average intensity and not on the total flux. For a given total light flux, the response is inversely porportional to the sensitive area. Since the noise currents are inversely proportional to the square root of the sensitive area,1 the attainable signal-to-noise ratio is also inversely proportional to the square root of the sensitive area.
Next consider a photoconductive cell used in a circuit like that shown in Fig. 2. Assume that the average light intensity / is sinusoidally varying as a function of time,
/ = B + C cos ut. (4)