Biophotonics_Concepts_to_Applications

The high electricfield present in the depletion region causes the carriers to separate
and be collected across the reverse-biased junction. This gives rise to a currentflow
in an external circuit, with one electronflowing for every carrier pair generated.
This currentflow is known as thephotocurrent.
As the charge carriersflow through the material, some electron–hole pairs will
recombine before they can be collected by the external circuit and hence will
disappear. On the average, the charge carriers move a distance Lnor Lpfor electrons
and holes, respectively. This distance is known as thediffusion length. The time it
takes for an electron or hole to recombine is known as thecarrier lifetimeand is
represented byτnandτp, respectively. The lifetimes and the diffusion lengths are
related by the expressions

Ln¼ðÞDnsn^1 =^2 ð 5 : 2 Þ

and

Lp¼ Dpsp

 1 = 2

ð 5 : 3 Þ

where Dnand Dpare theelectron diffusion coefficientandhole diffusion coefficient,
respectively, which are expressed in units of centimeters squared per second.
The dependence of the optical absorption coefficient on wavelength is shown in
Fig.5.3for several photodiode materials. As the curves show,αsdepends strongly
on the wavelength. Thus a particular semiconductor material can be used only over
a limited wavelength range. The upper wavelength cutoffλcis determined by the
bandgap energy Egof the material. If Egis expressed in units of electron volts (eV),
thenλcis given in units of micrometers (μm) by

Photogenerated electron

Photogenerated hole

Valence band

Conduction band

Depletion region

Photon

of energy

h Eg

Bandgap Eg

n region

i region

p region

+

Fig. 5.2 Simple energy-band diagram for apinphotodiode. Photons with energies greater than or
equal to Egcan generate free electron–hole pairs that become photocurrent carriers

122 5 Fundamentals of Optical Detectors