PHYSICAL PRINCIPLES OF PHOTODIODES 245Band gap Ρ FIGURE 6 2 Conduction
band Simple energy band diagram for a pin photodiode. Photons Photon
with an energy greater than or hv›Eg equal to the band gap energy J
—Depletion region—^ η Valence band Eg can generate free electron hole
pairs which act as photo current carriers.flow in an external circuit,
with one electron flowing for every carrier pairgenerated. This current
flow is known as the photocurrent. As the charge carriers flow through
the material, some electron hole pairswill recombine and hence
disappear. On the average, the charge carriers move adistance L„ or Lp
for electrons and holes, respectively. This distance is known asthe
diffusion length. The time it takes for an electron or hole to recombine
isknown as the carrier lifetime a n d is represented by Ï„„ and Ï„^,
respectively. Thelifetimes and the diffusiori lengths are related by the
expressions Ln = {D„Ï„„y^ and Lp = (DpTp)where D„ and Dp are the
electron and hole diffusion coefficients (or constants),respectively,
which are expressed in units of centimeters squared per second. Optical
radiation is absorbed in the semiconductor material according to
theexponential law Pix) = P o ( l e ) (6 1)Here, α^(λ) is the absorption
coefficient at a wavelength λ, PQ is the incident opticalpower level,
and P{x) is the optical power absorbed in a distance x. The dependence
of the optical absorption coefficient on wavelength isshown in Fig. 6 3
for several photodiode materials.^ As the curves clearlyshow, depends
strongly on the wavelength. Thus, a particular semiconductormaterial can
be used only over a limited wavelength range. The upper
wavelengthcutoff λc is determined by the band gap energy Eg of the
material. If Eg isexpressed in units of electron volts (eV), then λ^. is
given in units of micrometers(µm) by he _ 1.24 λ‚ (µm) =: = = (6 2) Eg
Eg(cW)The cutoff wavelength is about 1.06µm for Si and 1.6/xm for G e . F
o r longerwavelengths, the p h o t o n energy is not sufficient to
excite an electron from thevalence to the conduction band.
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