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Optical Fiber Communications [3rd ed]
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6.1

Band gap

PHYSICAL PRINCIPLES OF PHOTODIODES

Ρ

FIGURE 6-2 Conduction band

Simple energy-band diagram for a pin photodiode. Photons with an energy greater than or equal to the band-gap energy Eg can generate free electronhole pairs which act as photocurrent carriers.

Photon hv›Eg

J —Depletion region—^

η

Valence band

flow in an external circuit, with one electron flowing for every carrier pair generated. This current flow is known as the photocurrent. As the charge carriers flow through the material, some electron-hole pairs will recombine and hence disappear. On the average, the charge carriers move a distance L„ or Lp for electrons and holes, respectively. This distance is known as the diffusion length. The time it takes for an electron or hole to recombine is known as the carrier lifetime a n d is represented by τ„ and τ^, respectively. The lifetimes and the diffusiori lengths are related by the expressions Ln = {D„τ„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 the exponential law Pix) = P o ( l - e-

)

(6-1)

Here, α^(λ) is the absorption coefficient at a wavelength λ, PQ is the incident optical power level, and P{x) is the optical power absorbed in a distance x. The dependence of the optical absorption coefficient on wavelength is shown in Fig. 6-3 for several photodiode materials.'^ As the curves clearly show, depends strongly on the wavelength. Thus, a particular semiconductor material can be used only over a limited wavelength range. The upper wavelength cutoff λc is determined by the band-gap energy Eg of the material. If Eg is expressed in units of electron volts (eV), then λ^. is given in units of micrometers (µm) by he _ 1.24 λ ‚( µm) =:-=- = Eg-Eg(cW)

(6-2)

The cutoff wavelength is about 1.06µm for Si and 1.6/xm for G e . F o r longer wavelengths, the p h o t o n energy is not sufficient to excite an electron from the valence to the conduction band.

245