Page 44 - Photonics Essentials an introduction with experiments

Photodiodes

38 Photonic Devices

In this chapter, we will develop a model for the conversion of light
into electrical current by a photodiode. Along the way, we will also de-
velop a relationship for the current voltage relationship in a p-n junc-
tion. The p-n diode is a device that puts the Boltzmann relation to
work. So it is no surprise to find expressions like e – E/kT in the rela-
tionship between voltage and current. Without any voltage applied
across the terminals of a p-n junction, there is no current. In the lan-
guage of Boltzmann, the probability of finding a free electron on the p-
side of the junction is equal to the probability of finding a free electron
on the n-side. Thus, the energy difference must be zero. When a volt-
age is applied between the p-side and the n-side, the energy difference
is no longer zero, and so the probabilities are no longer the same. This
difference leads to a current in the diode.
The p-n junction is the basic device structure for all semiconductor op-
toelectronic devices, for example, lasers, LEDs, modulators, optical
switches, semiconductor optical amplifiers and so on. By characterizing
the electrical and optical properties of the p-n junction, much can be
learned about the internal composition and structure of the device, for
example, the band gap and the level of background impurities in the
material being used. This chapter includes results from suggested labo-
ratory experiments that are given in Chapter 11. The problems are large-
ly based on real data measured at the bench during these experiments.
The chapter reviews the fundamentals of photodiodes and their
electrical and optical properties (current–voltage relationship, quan-
tum efficiency, and spectral response).

3.2 The Current–Voltage Equation for Photodiodes

A silicon photodiode can absorb photons that have an energy greater
than the band gap [E g (Si) = 1.1 eV at room temperature]. Absorption
creates an electron in the conduction band and a hole in the valence
band. Most of this absorption takes place in neutral material, creating
one majority carrier and one minority carrier. The minority carrier will
diffuse to the p-n junction and be carried to the other side where it be-
comes a majority carrier, and contributes to the photocurrent. We can
determine the current–voltage relationship for a photodiode if we know
the functional dependence of the excess minority carrier concentration
as a function of position in the p-n junction. This depends on the ap-
plied voltage. The current can be obtained directly from the diffusion
equation
d
J = –qD n(x)
dx
In order to examine the details, let us consider the energy level dia-

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