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Light-Emitting Diodes
136 Photonic Devices
Figure 6.15. A simple model for the frequency dependence of an electronic device is
based on the idea that its response is frequency-independent up to a certain limit that
defines the bandwidth. Here we plot Eq. 6.40 as a function of frequency. The bandwidth
is defined as the frequency at which the response is one-half its original value.
6.9 Summary
The transient response of light-emitting diodes depends on the rela-
tionship of the injected excess carrier density to carrier concentration
introduced by doping. If the excess carrier density is less than the
doping level, the LED response time is independent of drive current,
and the rate equation can be solved explicitly for the light output as a
function of time. In this limit, the modulation of the carrier density by
the drive current has a negligible effect on equilibrium conditions in
the diode. The near-equilibrium carrier recombination time is the
equivalent to the LED rise time.
When the drive current introduces an excess carrier density com-
parable to the doping concentration, the transient response of the LED
depends on the drive current, with the response time becoming shorter
as the drive current is increased. Under these conditions, the LED rate
equation can be solved only by numerical methods to give the output
power as a function of time for a step change in the drive current. Under
the assumption of a small ac modulation amplitude around a dc operat-
ing point, we were able to derive a simple expression for the modulation
bandwidth. This expression shows that the ac modulation bandwidth
increases as the square root of the dc operating point current.
6.10 Review of Important Concepts
Efficient LEDs are commercially available in red, green, and blue for
full-color (RGB) visual displays and for lighting applications. LEDs
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