Page 13 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Photodetection Basics

6 Chapter One

speed. Finally, additional high dopant concentration diffusions are performed
to allow low-resistance “ohmic contact” connections to the top layer and
substrate to be made for subsequent bonding of metal leads. We will return to
this design in discussions of the sensitivity and wavelength characteristics of
photodiodes.

1.5 Responsivity: What Current per Optical Watt?
Earlier we assumed that one photon generates one hole-electron pair. This is
because detection in a photodiode, like the photoelectric effect at a vacuum-
metal interface, is a quantum process. In an ideal case each photon with an
energy greater than the semiconductor bandgap energy will generate precisely
one hole-electron pair. Therefore, neglecting nonlinear multiphoton effects, the
charge generated on photodetection above the bandgap is independent of
photon energy. The photodiode user is generally most interested in the inter-
nal current (I o) that is generated for each received watt (P r) of incident light
power. This is termed the responsivity (r) of the photodiode, with units of
ampere per watt (A/W):

r = I o (1.1)
P r
However, we will see later that the noise performance of the designer’s circuitry
is more a function of the arrival rate of photons at his detector and the total
number of photoelectrons counted during his experiment. It is important to
remember that detection is a quantum process, with the generation of discrete
units of charge. As the energy of a photon (hc/l) is inversely proportional to its
wavelength, the number of photons arriving per second per watt of incident
power is linearly proportional to the wavelength, and the responsivity of an
ideal photodiode increases with wavelength. For this ideal case we can write:
ql
r ideal l () = I o = (1.2)
P r hc
where l = is the wavelength of the incident light in meters
q = 1.602 ¥ 10 -19 C is the charge on the electron
2
h = 6.626 ¥ 10 -34 Ws is Planck’s constant
8
c = 2.998 ¥ 10 m/s is the speed of light in vacuum
For example, at a wavelength of 0.78mm, the wavelength of the laser diode in
a music CD player, r ideal = 0.63mA/mW. So for a laser diode that emits 1mW or
so, the change of units for responsivity into milliamperes per milliwatt is con-
venient and gives an immediate idea of the (ª mA) photocurrent generated by
its internal monitor diode. This is the responsivity for 100 percent quantum
efficiency and for 100 percent extraction of the photocurrent.
Again with a view to obtaining expressions that can be used quickly in mental
arithmetic, the wavelength can be expressed in microns to give:

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