Page 172 - Photonics Essentials an introduction with experiments

Lasers

166 Photonic Devices

to the peak of the gain distribution. We can use this approximation to
make a practical estimate of the threshold current density:

2 2
qtN th k th n f max f
21
J th = = qt A-cm –2
2
r r c
or
2
21
qtN th k th n f
J th = = qt A-cm –2 (7.23)
2
r r max
All the variables in this expression are easily accessible. The width of
the recombination region, t, is controlled during fabrication. In a het-
erostructure laser, this is typically about 10 –5 cm, and in a quantum
well laser, about one order of magnitude less, or ~ 10 –6 cm. We esti-
mated k th in Exercise 7.2. The width of the gain spectrum in energy is
about 0.02 eV, and can be estimated from the emission spectrum in
the middle frame of Fig. 7.11. The peak of the gain curve occurs at an
energy close to the band gap energy. The ratio of the luminescence
time to the recombination time is always greater than 1 because the
recombination time includes both radiative and nonradiative recombi-
nation modes, as you will recall from the discussion of light-emitting
diode rise time in Chapter 6. However, in a reasonably good laser, this
ratio is close to 1.
The equation we developed for the threshold current can be used
as a model to show the dependence of the threshold current on ma-
terial parameters. This model does a good job of estimating the
threshold current in semiconductor laser materials based on GaAs
and InP. A typical value for the threshold current of GaAs-based
–2
heterostructure lasers is about 3 kA-cm . A GaAs laser with a
threshold twice this high will not work in continuous operation at
room temperature.

Figure 7.11. Light emission from a GaAs/AlGaAs laser structure at room temperature.
In (a), the laser device is operating in the LED mode. The emission line width is deter-
mined by the density of states and the relative transparency of the diode for photon en-
ergies higher than the band gap. In (b), the first effects of gain can be seen. The emis-
sion linewidth narrows and centers on the energy region where the gain is highest,
which occurs at a slightly lower energy. In (c), the current is above threshold, and light
emission occurs in only a few resonant cavity modes where the gain is highest. A wave-
length marker shows the linewidth (~ 1.5 Å) and the spacing (~ 3 Å) of these modes.
This is close to the resolution (~ 0.5 Å) of a 0.25 m spectrometer at this wavelength. (Re-
produced with permission from H. C. Casey, Jr. and M. B. Panish, Heterostructure
Lasers, Part A, p. 179, Academic Press, New York, 1978.)

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