Page 134 - Photonics Essentials an introduction with experiments
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Light-Emitting Diodes
128 Photonic Devices
1.0 m
0.1 m
100 m
emitted light
Figure 6.14. A schematic diagram of an edge-emitting LED showing some typical phys-
ical dimensions.
J N
= B( N + n D ) N +
qd n–r
N
2
= B N + B Nn D +
n–r
This is a quadratic equation for N:
1 J
2
B N + N Bn D + – = 0
n–r qd
1 1 2 J
Bn D +
+ 4B
– Bn D + +
q
d
n–r n–r
N =
2B
Substitute values and solve for N:
N = 1.67 × 10 19 cm –3 ( N > n D )
N = N + n D = 1.67 × 10 19 + 5 × 10 17 1.7 × 10 19 cm –3
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