Page 133 - Photonics Essentials an introduction with experiments

Light-Emitting Diodes

Light-Emitting Diodes 127

Using this equation, we can now simplify the expression for the LED
output power in Eq. (6.15) so that the optical output power is ex-
pressed in terms of the drive current:
2
P out = ext · V·B(NP – n i )·
J
= ext · V· int
qd

I
I
= ext · int · · = (6.25)
q q
The overall quantum efficiency of the LED is defined as:
number of photons out

number of electrons in
P opt · q
P opt
= = (6.26)
(I/q) · I

Example 6.4. Steady-State Analysis of an LED
A light-emitting diode with a length of 100 m having an emitting
stripe width of 1 m is driven by a current step of 50 mA. The thick-
ness of the emission region is 0.1 m. Some of the other properties of
the diode are listed below (see Fig. 6.14):

I = 50 mA
= 1.35 m
ext = 0.1
n–r = 2 × 10 –9 sec
3
B = 8 × 10 –11 cm /sec
n D = 5 × 10 17 cm –3

Find the excess carrier density, the radiative recombination rate, the
internal quantum efficiency and the steady-state output power of the
LED.
First, write down the expression for the steady state electrical
pumping rate:

J 1
= BN(N – n D ) + (N – n D )
qd n–r
Next, rewrite this equation in terms of the excess carrier density,
N = N – n D :

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