23.4 Lasers
673
To this equation, the factor η int must be added. The internal quantum efficiency describes the efficiency
of the conversion of electron–hole pairs into photons (cmp. (10.59)):
η int =
B n
2
+ v g g thr N ph
A n + B n 2 + C n 3 + v g g thr N ph
.
(23.32)
All in all, now (see Fig. 23.49a)
P out =
ω
e
α m
α m + α i
η int (I − I thr ) .
(23.33)
The differential (or slope) quantum efficiency, also called the external quantum efficiency η ext , is the
slope of the P out curve versus the current in the lasing regime. It is given by
η ext =
d P out /dI
ω/e
= η int
α m
α m + α i
.
(23.34)
The external quantum efficiency can also be written as
1
η ext
=
1
η int
1 +
α i
α m
=
1
η int
[1 − 2α i L ln (R 1 R 2 )] .
(23.35)
Therefore, if η
−1
ext is plotted for similar lasers with different cavity length (see Fig. 23.45b), a straight
line should arise from which the internal quantum efficiency (extrapolation to L → 0) and the internal
loss (∝ slope) can be determined experimentally.
The threshold current for a given laser is typically determined from the P–I characteristic via
extrapolation of the linear regime as shown in Fig. 23.49a. Other measures of the threshold current can
be the change in junction resistance, the narrow peak in excess noise or the peak in the logarithmic
derivative of mode power. The S-shaped curve of the power in the dominant mode (of a single-mode
laser) as a function of voltage (Fig.23.48), similar to the S-shaped curves of Fig.23.47 has been discussed
in [1992]. A related discussion of laser dynamics (cmp. Sect. 23.4.13) can be found in [1993].
Record values for the threshold current density are often given for the limit L → ∞. Due to current
spreading, the threshold current density also depends on the width of the injection stripe. Record low
thresholds are therefore often given for the limit w → ∞.
The total quantum efficiency is given by
η tot =
P out /I
ω/e
.
(23.36)
This quantity is shown in Fig. 23.49b for a laser as a function of the current. For a linear P–I lasing
characteristic, the total quantum efficiency converges towards the external quantum efficiency for high
currents because the low quantum efficiency subthreshold regime no longer plays any role. Another
important figure of merit is the wall-plug efficiency η w that describes the power conversion:
η w =
P out
U I
.
(23.37)
Additionally to the current balance discussed so far, typically a leakage current exists that flows without
contributing to recombination or lasing. Carriers not captured into or escaping from the active layers
can contribute to this current. The present record for wall-plug efficiency of high-power laser diodes
is above 70% [1994, 1995], employing careful control of band alignment (graded junctions, avoiding
673
To this equation, the factor η int must be added. The internal quantum efficiency describes the efficiency
of the conversion of electron–hole pairs into photons (cmp. (10.59)):
η int =
B n
2
+ v g g thr N ph
A n + B n 2 + C n 3 + v g g thr N ph
.
(23.32)
All in all, now (see Fig. 23.49a)
P out =
ω
e
α m
α m + α i
η int (I − I thr ) .
(23.33)
The differential (or slope) quantum efficiency, also called the external quantum efficiency η ext , is the
slope of the P out curve versus the current in the lasing regime. It is given by
η ext =
d P out /dI
ω/e
= η int
α m
α m + α i
.
(23.34)
The external quantum efficiency can also be written as
1
η ext
=
1
η int
1 +
α i
α m
=
1
η int
[1 − 2α i L ln (R 1 R 2 )] .
(23.35)
Therefore, if η
−1
ext is plotted for similar lasers with different cavity length (see Fig. 23.45b), a straight
line should arise from which the internal quantum efficiency (extrapolation to L → 0) and the internal
loss (∝ slope) can be determined experimentally.
The threshold current for a given laser is typically determined from the P–I characteristic via
extrapolation of the linear regime as shown in Fig. 23.49a. Other measures of the threshold current can
be the change in junction resistance, the narrow peak in excess noise or the peak in the logarithmic
derivative of mode power. The S-shaped curve of the power in the dominant mode (of a single-mode
laser) as a function of voltage (Fig.23.48), similar to the S-shaped curves of Fig.23.47 has been discussed
in [1992]. A related discussion of laser dynamics (cmp. Sect. 23.4.13) can be found in [1993].
Record values for the threshold current density are often given for the limit L → ∞. Due to current
spreading, the threshold current density also depends on the width of the injection stripe. Record low
thresholds are therefore often given for the limit w → ∞.
The total quantum efficiency is given by
η tot =
P out /I
ω/e
.
(23.36)
This quantity is shown in Fig. 23.49b for a laser as a function of the current. For a linear P–I lasing
characteristic, the total quantum efficiency converges towards the external quantum efficiency for high
currents because the low quantum efficiency subthreshold regime no longer plays any role. Another
important figure of merit is the wall-plug efficiency η w that describes the power conversion:
η w =
P out
U I
.
(23.37)
Additionally to the current balance discussed so far, typically a leakage current exists that flows without
contributing to recombination or lasing. Carriers not captured into or escaping from the active layers
can contribute to this current. The present record for wall-plug efficiency of high-power laser diodes
is above 70% [1994, 1995], employing careful control of band alignment (graded junctions, avoiding