Page 20 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Photodetection Basics

Photodetection Basics 13

1.7.3 Short circuit operation
If, alternatively, the diode is operated into a short circuit, we have V d = 0. With
no voltage, no current can flow through the internal diode, and the full
internally generated photocurrent is available at the output terminals. Then
the bracketed quantity in Eq. 1.6 is zero, and internal and external currents
are equal. Now the external current is linearly related to the incident power.
This linearity can hold over at least 6 or even 10 orders of magnitude of inci-
dent power. At the very lowest detectable photocurrents, that is, for a small
ratio of I o /I s , the presence of I s cannot be neglected. At the other end of the scale
photodiodes cannot handle arbitrarily large photocurrents. At high currents the
photodiode series resistance shown in Fig. 1.7 contributes a voltage drop,
diverting some of the internal photocurrent through the diode and through R sh.
Hence linearity can suffer. Fine wire bonds can even be melted. Photodiodes
are usually specified with limits either on total power (mW) or power density
2
(mW/mm ). With focussed laser sources these limits can easily be reached,
leading to odd behavior.
Equations (1.7) and (1.8) suggest that the photocurrent decreases and the
open circuit voltage increases with increasing temperature. This is not the case
experimentally observed. For example, the data sheet of the popular BPX65
photodiode (manufactured by Infineon, part of the Siemens group, and others)
shows a short circuit temperature coefficient for external current of the order
of +0.2 percent/°C. This can be explained by noting that reverse saturation
current is also an exponential function, increasing with temperature:

I s ª e - E g kT (1.9)

1.7.4 General operation
Apart from the open and short circuit configurations, the photodiode may in
general be operated with a finite load resistor varying over a wide range of
values and with an applied voltage in forward or reverse bias. Hence it is useful
to be able to calculate the output current and voltage under any such condi-
tions. This is a little trickier than for the open and short circuit conditions; one
approach is given here. In Fig. 1.8 we generalize the circuit and add a bias
voltage source V b in series with the load resistor R L . Then we can write two
expressions for I p, one from the internal diode components and one from the
external circuit:
V d -
I p = V b (1.10)
R L
I p = I o - I d (1.11)
◊ (e ◊ qV d ◊ kT - ) 1 (1.12)
= I o - I s
Changing I s to I s ¢ to give a more realistic temperature dependence of Eq. (1.9):

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