Page 21 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Photodetection Basics

14 Chapter One

Photodiode
I p R L

A
I o I d
V b
"Internal" V d
photocurrent Ideal
generator
diode
K

Figure 1.8 The photodiode’s terminal voltage can be obtained
by solving the circuit equations given the external bias
voltage and load resistor.

¢
I p = I o - I e - qE g kT e ( qV d kT - ) 1 (1.13)
s
Equate the two expressions and rearrange:

(
)
¢
FV d = I o - I e - qE g kT e ( qV d kT - ) - V d + V b = 0 (1.14)
1
s
R L R L
To solve this for V d we can either plot the function and just look for the zero
or use Newton’s method to iteratively generate new estimates of V d:
( )
= - FV d Z (1.15)
¢( )
V d Z+1 V d Z
FV d Z
where F¢(V d) is the derivative of F(V d) with respect to V d. With a few iterations,
this usually converges on a solution for the diode voltage V d and hence for the
®
other currents and voltages. With the mathematical software Mathcad * we can
just solve for V d using something like V d = 0, solution:= root(F(V d ),V d ). Note that
this works for forward and reverse bias, with and without photocurrents, and
so can be used in all three quadrants of the photodiode characteristics.
Figure 1.9 shows the complete schematic current/voltage characteristic of a
photodiode under three levels of illumination. In the first quadrant (positive
voltage and current) the curve labeled “dark” is just the exponential forward
characteristic of a junction diode. In the third quadrant only a very small
current flows (I s). As the level of incident light is increased, the curves shift
bodily downward in the negative current direction. This shift is linear in inci-
dent power, as is the set of points on the V = 0 axis marked I SC (short circuit).
The zero current points marked V OC (open circuit) are clearly a nonlinear func-
tion of illumination, as discussed earlier. At very high reverse bias voltages the
current may increase rapidly to large and possibly damaging values. This is the
reverse breakdown region.

*Mathcad is a registered trademark of Mathsoft Engineering and Education Inc.
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