3.2. LIGHT-EMITTING DIODES 89
Figure 3.7: (a) Power–current curves at several temperatures; (b) spectrum of the emitted light
for a typical 1.3-μm LED. The dashed curve shows the theoretically calculated spectrum. (After
Ref. [21];©c1983 AT&T; reprinted with permission.)
Another quantity sometimes used to characterize the LED performance is there-
sponsivitydefined as the ratioRLED=Pe/I. From Eq. (3.2.2),
RLED=ηextηint( ̄hω/q). (3.2.6)A comparison of Eqs. (3.2.5) and (3.2.6) shows thatRLED=ηtotV 0. Typical values
ofRLEDare∼ 0 .01 W/A. The responsivity remains constant as long as the linear re-
lation betweenPeandIholds. In practice, this linear relationship holds only over a
limited current range [21]. Figure 3.7(a) shows the power–current (P–I) curves at sev-
eral temperatures for a typical 1.3-μm LED. The responsivity of the device decreases
at high currents above 80 mA because of bending of theP–Icurve. One reason for
this decrease is related to the increase in the active-region temperature. The internal
quantum efficiencyηintis generally temperature dependent because of an increase in
the nonradiative recombination rates at high temperatures.
3.2.2 LED Spectrum
As seen in Section 2.3, the spectrum of a light source affects the performance of op-
tical communication systems through fiber dispersion. The LED spectrum is related
to the spectrum of spontaneous emission,Rspon(ω), given in Eq. (3.1.10). In general,
Rspon(ω)is calculated numerically and depends on many material parameters. How-
ever, an approximate expression can be obtained ifA(E 1 ,E 2 )is assumed to be nonzero
only over a narrow energy range in the vicinity of the photon energy, and the Fermi
functions are approximated by their exponential tails under the assumption of weak