664
23 Electricity-to-Light Conversion
(a)
(b)
Fig. 23.35 a Gain spectra of a 6.8 nm thick Ga 0.41 In 0.59 P/(Al 0.5 Ga 0.5 ) 0.51 In 0.49 P quantum well, experimental data
(symbols) and theory (lines) for three different sheet carrier densities n 2D = 2.2, 2.7, and 3.2 × 10 12 cm −2 . b Maximum
gain as a function of the separation of the quasi-Fermi levels, experimental data (symbols) and theory (lines). Adapted
from [1980]
g(n) ∼ = ˆ
α
n − n tr
n tr
.
(23.13)
For large carrier density, the gain saturates (at a value similar to α). The onset of positive gain is related
to the separation of the quasi-Fermi levels being larger than the band gap (23.10), Fig. 23.35b. The
gain in quantum dot lasers [150] has been discussed in [1981].
23.4.4 Optical Mode
The light wave that is amplified must be guided in the laser. An optical cavity is needed to provide
optical feedback such that the photons travel several times through the gain medium and contribute to
amplification. We explain the light-wave management for the edge emitter first:
Vertical Mode Guiding
In the course of the historical development of the semiconductor laser, the most significant improvements (reduction of lasing threshold current) have been achieved through the improvement of the
overlap of the optical wave with the gain medium, as shown in Fig.23.36. From homojunctions over
the single heterojunction, eventually the double heterostructure (DHS) design could reduce the laser
threshold current density to the 1 kA/cm
2 level.
The band diagram of a double heterostructure is shown in Fig. 23.37 for zero and forward bias. In
the DHS, the optical mode is guided by total reflection within the low band gap center layer (core),
which has a larger index of refraction than the outer, large band gap layer (cladding).
19 When the layer
thickness is in the range of λ/n r , the form of the optical mode is determined by the (one-dimensional)
wave equation (19.3) for the electrical field E z . In Fig.23.38a, the shape of the optical mode for
GaAs/Al 0.3 Ga 0.7 As DHS with different GaAs thickness is shown.
The optical confinement factor is the part of the wave that has geometrical overlap with the gain
medium, i.e. is subject to amplification. It is shown for GaAs/Al x Ga 1−x As DHS with different GaAs
thickness and different Al concentration in Fig. 23.38b. The modal gain g mod that is responsible for
light amplification in the cavity consists of the material gain g mat due to inversion and the optical
confinement factor.
19 A smaller band gap coincides in many cases with a larger index of refraction.
23 Electricity-to-Light Conversion
(a)
(b)
Fig. 23.35 a Gain spectra of a 6.8 nm thick Ga 0.41 In 0.59 P/(Al 0.5 Ga 0.5 ) 0.51 In 0.49 P quantum well, experimental data
(symbols) and theory (lines) for three different sheet carrier densities n 2D = 2.2, 2.7, and 3.2 × 10 12 cm −2 . b Maximum
gain as a function of the separation of the quasi-Fermi levels, experimental data (symbols) and theory (lines). Adapted
from [1980]
g(n) ∼ = ˆ
α
n − n tr
n tr
.
(23.13)
For large carrier density, the gain saturates (at a value similar to α). The onset of positive gain is related
to the separation of the quasi-Fermi levels being larger than the band gap (23.10), Fig. 23.35b. The
gain in quantum dot lasers [150] has been discussed in [1981].
23.4.4 Optical Mode
The light wave that is amplified must be guided in the laser. An optical cavity is needed to provide
optical feedback such that the photons travel several times through the gain medium and contribute to
amplification. We explain the light-wave management for the edge emitter first:
Vertical Mode Guiding
In the course of the historical development of the semiconductor laser, the most significant improvements (reduction of lasing threshold current) have been achieved through the improvement of the
overlap of the optical wave with the gain medium, as shown in Fig.23.36. From homojunctions over
the single heterojunction, eventually the double heterostructure (DHS) design could reduce the laser
threshold current density to the 1 kA/cm
2 level.
The band diagram of a double heterostructure is shown in Fig. 23.37 for zero and forward bias. In
the DHS, the optical mode is guided by total reflection within the low band gap center layer (core),
which has a larger index of refraction than the outer, large band gap layer (cladding).
19 When the layer
thickness is in the range of λ/n r , the form of the optical mode is determined by the (one-dimensional)
wave equation (19.3) for the electrical field E z . In Fig.23.38a, the shape of the optical mode for
GaAs/Al 0.3 Ga 0.7 As DHS with different GaAs thickness is shown.
The optical confinement factor is the part of the wave that has geometrical overlap with the gain
medium, i.e. is subject to amplification. It is shown for GaAs/Al x Ga 1−x As DHS with different GaAs
thickness and different Al concentration in Fig. 23.38b. The modal gain g mod that is responsible for
light amplification in the cavity consists of the material gain g mat due to inversion and the optical
confinement factor.
19 A smaller band gap coincides in many cases with a larger index of refraction.