4.2 Principles of Light-Emitting Diodes (LEDs)
167
the nonradiative recombination rate is R nr , then the internal quantum efficiency η int
is the ratio of the radiative recombination rate to the total recombination rate:
η int =
R r
R r + R nr
(4.9)
For exponential decay of excess carriers, the radiative recombination lifetime is τ r
= n/R r and the nonradiative recombination lifetime is τ nr = n/R nr . Thus the internal
quantum efficiency can be expressed as
η int =
1
1 +
τ r
τ nr
=
τ
τ r
(4.10)
where the bulk recombination lifetime τ is
1
τ
=
1
τ r
+
1
τ nr
(4.11)
In general, τ r and τ nr are comparable for direct-bandgap semiconductors, such
as GaAlAs and InGaAsP. This also means that R r and R nr are similar in magnitude, so that the internal quantum efficiency is about 50 percent for simple homojunction LEDs. However, LEDs having double-heterojunction structures can have
quantum efficiencies of 60−80%. This high efficiency is achieved because the thin
active regions of these devices mitigate the self-absorption effects, which reduces
the nonradiative recombination rate.
If the current injected into the LED is I, then the total number of recombinations
per second is
R r + R nr = I/q
(4.12)
Substituting Eq. (4.12) into Eq. (4.9) then yields R r = η int I/q. Noting that R r is
the total number of photons generated per second and that each photon has an energy
hν, then the optical power generated internally to the LED is
P int = η int
I
q
hν = η int
hcI
qλ
(4.13)
Example 4.5 Suppose that a double-heterojunction InGaAsP LED emitting at a
peak wavelength of 1310 nm has radiative and nonradiative recombination times of
30 and 100 ns, respectively, and let the drive current be 40 mA. Find (a) the bulk
recombination time; (b) the internal quantum efficiency; and (c) the internal power
level.
Solution (a) From Eq. (4.11), the bulk recombination lifetime is
167
the nonradiative recombination rate is R nr , then the internal quantum efficiency η int
is the ratio of the radiative recombination rate to the total recombination rate:
η int =
R r
R r + R nr
(4.9)
For exponential decay of excess carriers, the radiative recombination lifetime is τ r
= n/R r and the nonradiative recombination lifetime is τ nr = n/R nr . Thus the internal
quantum efficiency can be expressed as
η int =
1
1 +
τ r
τ nr
=
τ
τ r
(4.10)
where the bulk recombination lifetime τ is
1
τ
=
1
τ r
+
1
τ nr
(4.11)
In general, τ r and τ nr are comparable for direct-bandgap semiconductors, such
as GaAlAs and InGaAsP. This also means that R r and R nr are similar in magnitude, so that the internal quantum efficiency is about 50 percent for simple homojunction LEDs. However, LEDs having double-heterojunction structures can have
quantum efficiencies of 60−80%. This high efficiency is achieved because the thin
active regions of these devices mitigate the self-absorption effects, which reduces
the nonradiative recombination rate.
If the current injected into the LED is I, then the total number of recombinations
per second is
R r + R nr = I/q
(4.12)
Substituting Eq. (4.12) into Eq. (4.9) then yields R r = η int I/q. Noting that R r is
the total number of photons generated per second and that each photon has an energy
hν, then the optical power generated internally to the LED is
P int = η int
I
q
hν = η int
hcI
qλ
(4.13)
Example 4.5 Suppose that a double-heterojunction InGaAsP LED emitting at a
peak wavelength of 1310 nm has radiative and nonradiative recombination times of
30 and 100 ns, respectively, and let the drive current be 40 mA. Find (a) the bulk
recombination time; (b) the internal quantum efficiency; and (c) the internal power
level.
Solution (a) From Eq. (4.11), the bulk recombination lifetime is