Page 129 - Photonics Essentials an introduction with experiments

Light-Emitting Diodes

Light-Emitting Diodes 123

changeover. If you aim to recover your costs in 8 years, you can
pay $480 per LED light and still face your voters. This repre-
sents the net present value of the cash flows of $73 each year for
the next 8 years, discounted at 5%.

6.6 Response Time
The light-emitting diode is based on two considerations: the intrinsic
recombination lifetime of injected excess carriers, and the extrinsic
RC time calculated from the diode capacitance in forward bias and its
series resistance. This RC time, representing the time necessary to
charge the diode capacitance is usually the dominant factor determin-
ing the modulation speed of LEDs.
The series resistance of an LED is determined by the majority carri-
er doping and the conductivity of the substrate on one hand, and pro-
cessing-related features, such as ohmic contact resistance on the oth-
er. The typical series resistance found in commercial LEDs is a few
ohms. The capacitance is the diffusion capacitance. Simple models for
this capacitance are too inaccurate to be used even for estimates. Both
parameters should be measured. For the high-brightness red LED
shown in Fig. 6.4, this capacitance is 250 pF under operating condi-
tions. The RC time constant is 1.25 · 10 –9 sec, giving a modulation
bandwidth of about 120 MHz.
In the following sections, we will formulate a model of the LED
based on rate equations that describe the transient behavior of the ex-
cess carrier concentration. This approach is an important stepping
stone toward the description of the response time and modulation rate
of semiconductor lasers. To make a long story short, the intrinsic
modulation bandwidth of LEDs depends on the carrier concentration
of electrons and holes in the region where recombination takes place.

6.7 Steady-State Input Electrical Current and
Output LED Optical Power
Light output cannot respond simultaneously to the electrical input
signal. There are delays associated with the buildup of the nonequi-
librium carrier concentration that is in competition with recombina-
tion. Both nonradiative and radiative recombination are important.
Our treatment is based on the rate equation that shows how the num-
ber of charge carriers changes with time.
The modulation rate for the LED reflects the rate at which the car-
rier concentration can be changed. The carrier concentration consists
of an equilibrium component, created by doping, and a nonequilibri-

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