Experimental investigation of the effect of wetting-layer states on the gain–current
characteristic of quantum-dot lasers
D. R. Matthews, H. D. Summers, P. M. Smowton, and M. Hopkinson
Citation: Applied Physics Letters 81, 4904 (2002); doi: 10.1063/1.1532549
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Experimental investigation of the effect of wetting-layer states on the
gain–current characteristic of quantum-dot lasers
D. R. Matthews,
a)
H. D. Summers, and P. M. Smowton
Department of Physics and Astronomy, Cardiff University, Cardiff CF24 3YB, United Kingdom
M. Hopkinson
EPSRC Central Facility for III-V Semiconductors, University of Sheffield, Sheffield S1 3JD, United Kingdom
共Received 30 September 2002; accepted 30 October 2002兲
Using experimental measurements of the gain–current characteristic as a function of temperature in
InGaAs quantum-dot lasers, we demonstrate that it is the population of wetting-layer states that
leads to a saturation of the population inversion in dot states and hence to the saturation of gain in
a quantum-dot laser. At 300 K, the maximum modal gain for a three-layer structure is reduced from
53 to 14 cm
⫺1
.©2002 American Institute of Physics. 关DOI: 10.1063/1.1532549兴
The impetus to develop quantum-dot 共QD兲 lasers has
come from the numerous performance improvements pre-
dicted for a zero-dimensional system, for example, a thresh-
old current independent of temperature, zero linewidth en-
hancement factor, and extremely high differential gain.
1–3
In
practice, dot lasers have delivered significant benefits rela-
tive to quantum-well devices,
4–6
and their potential for ap-
plications such as femtosecond pulse generation over a wide
wavelength range
7
is of increasing interest. However, in re-
ality dots cannot be treated as isolated zero-dimensional sys-
tems. In the Stranski–Krastinov self-assembled material,
used for semiconductor lasers, the dots are sited within a
wetting layer, and this has a major influence on the laser
performance. The localized QD states and the two-
dimensional wetting-layer states must be considered as an
electronically coupled system. Within this system, the carrier
distribution in the dot states is mediated by the wetting-layer
states. The number of accessible two-dimensional 共2-D兲
states can be as much as two orders of magnitude greater
than those in the dots, so that the influence of the wetting
layer can be extremely marked.
Theoretical models of QD lasers have already shown
how the presence of higher energy states, both within the
dots themselves and in the wetting layer, influence dot laser
performance, increasing the threshold current,
8
reducing the
available gain
9
and damping the frequency response.
10
In this
letter, we present detailed experimental measurements of the
saturation of the QD laser gain–current relationship as a
function of temperature, and show that the saturation results
from occupancy of high lying energy states rather than com-
plete population inversion of the available dot states. A the-
oretical treatment of the degree of carrier inversion within
these lasers shows that the large wetting-layer density of
states 共DOS兲 acts as a source of inertia, slowing the move-
ment of the Fermi levels as charge is injected. The damping
of the differential gain that this produces is in agreement
with the experimental results.
The laser structures contain three layers of InGaAs QDs
formed by depositing 2.1 nm of InGaAs on 100 nm of
Al
0.15
Ga
0.85
As. Barrier layers of Al
0.15
Ga
0.85
As, 7 nm wide,
separate each layer of QDs. The wafer was processed into
8-
m-wide, ridge lasers and nonlasing test devices with seg-
mented contacts of 300
m length. The emission wavelength
of the 1200-
m-length lasers was 1000 nm at 300 K. The
modal gain of pumped material or, in a separate experiment,
the absorption of unpumped laser material, is measured using
a modified version of the variable stripe length method in
which the gain length is altered by electrically injecting dif-
ferent sections of the device.
11
The amplified, single-pass
spontaneous emission is collected via a 0.3 m spectrometer,
thus allowing us to collect full gain or absorption spectra.
Typical results are shown in Fig. 1. The high degree of in-
homogeneous broadening in these dot samples produces a
continuous gain spectrum over 200 nm in width, within
which the ground and excited dot states cannot be resolved.
The large variation in dot size also effects the absorption
spectra of the lasers, producing a shallow absorption edge.
From the gain spectra, we can extract the modal gain as a
function of injected current. Plots of the gain versus current,
achieved at the lasing wavelength, are shown in Fig. 2 for a
range of temperatures. At all temperatures there is strong
a兲
Electronic mail: matthewsdr2@cf.ac.uk
FIG. 1. Typical modal gain and absorption spectra at 300 K 共triangular and
square symbols, respectively兲. Also shown is an absorption spectrum at 100
K 共circular symbols兲. At the 300 K lasing wavelength 共1000 nm兲, the ab-
sorption is ⬃58 cm
⫺1
compared to the modal gain of ⬃14 cm
⫺1
. At the 100
K lasing wavelength 共960 nm兲, the absorption takes a value of ⬃49 cm
⫺1
,
which is very close to the saturated modal gain value of 53 cm
⫺1
.
APPLIED PHYSICS LETTERS VOLUME 81, NUMBER 26 23 DECEMBER 2002
49040003-6951/2002/81(26)/4904/3/$19.00 © 2002 American Institute of Physics
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saturation of the gain at higher values of the injection cur-
rent. Such saturation is expected in a QD system due to the
finite number of electronic states. However, as the tempera-
ture is decreased, the maximum value of the gain increases,
thus indicating that the saturation effect is not due to the
complete occupancy of the dot states. We show later that
such saturation, where the maximum gain increases with de-
creasing temperature, is consistent with the presence of a
populated wetting layer with a larger number of states than
the QDs. Additional current density at constant temperature
increases the population of the wetting layer, but does not
significantly change the Fermi-level position or the popula-
tion of the dot states. At a temperature of 100 K, the gain–
current curve shows distinctly different behavior. The gain
increases linearly until it reaches a maximum value and then
abruptly saturates. At this low temperature, the rate at which
carriers thermally escape from the dots to the wetting layer is
significantly decreased, and this effectively decouples the
dots from both the wetting layer and each other. Thus, carri-
ers are no longer thermally distributed among the QD states,
and the system can no longer be described by Fermi–Dirac
statistics. In this regime, the occupancy of the dots increases
with increasing current density as carriers are randomly cap-
tured, and will saturate when the occupancy becomes com-
plete. The gain–current characteristic at 100 K in Fig. 2 is
consistent with this explanation and in agreement with theo-
retical models of dot lasers at low temperature.
12
Further verification of this interpretation of the experi-
ment is provided by the absorption data in Fig. 1. The ab-
sorption and gain of the system are given by the same ex-
pression related to the interaction matrix element, number of
states, and occupancies of the conduction and valence band
electron states. Thus, the magnitude of the absorption, corre-
sponding to a valence band occupancy of 1 and conduction
band occupancy of 0 is equal to the maximum gain achiev-
able by completely inverting the carrier population within
the dots. At 100 K, where the saturation of the gain occurs
due to complete occupation of the available dot states, there
is a saturated gain value of 53⫾ 5cm
⫺ 1
at high currents in
Fig. 2. The absorption value at 100 K at the lasing and mea-
surement wavelength of 960 nm is 49⫾ 3cm
⫺ 1
. Thus, within
the error bounds of the experiment, the absorption and maxi-
mum gain are of the same magnitude. However, at 300 K,
where the saturation of the gain is due to a saturated Fermi
level, the gain value of 14⫾ 5cm
⫺ 1
is significantly less than
the absorption value of 58⫾ 3cm
⫺ 1
at the lasing wavelength
of 1000 nm.
Figure 3 shows an estimate of the DOS for the dots and
the wetting layer. The density of wetting-layer states is sim-
ply calculated assuming a 2-D electron gas in the wetting
layer, and this is represented by the rectangular functions in
Fig. 3. The relative energies of the dot and wetting-layer
states are calculated assuming a conduction band/valence
band offset ratio of 60/40 and solving the Schro
¨
dinger equa-
tion for lens-shaped dots.
13
Due to the zero-dimensional na-
ture of the QDs, their energy states should be represented in
terms of number rather than density. However, for the pur-
pose of comparison, an equivalent DOS has been plotted in
Fig. 3, assuming a dot coverage of 2⫻ 10
10
dots cm
⫺ 2
and a
full width at half maximum of 50 meV for the dot inhomo-
geneous broadening. The heavier hole mass produces a
Gaussian distribution of states that is much narrower than
that of the electron states. The integral area under the Gauss-
ian distributions, in Fig. 3, corresponds to the total available
QD states. It should be noted that the graph is plotted on a
logarithmic scale and that there is at least a two orders of
magnitude difference in the number of available states in the
wetting layer compared to the dots. By calculating the con-
volution of the DOS and Fermi-functions we can calculate
the total carrier density for a given Fermi energy. We then
obtain the occupancy of the QD states as a function of carrier
density. It is the difference in the occupancy of the conduc-
tion and valence states, f
c
⫺ f
v
, at the lasing energy, that
determines the gain available in a laser device. Figure 4
shows a plot of f
c
⫺ f
v
as a function of the total carrier den-
sity. This confirms that the large number of wetting-layer
states damps the movement of the Fermi energy and so com-
plete population inversion (f
c
⫺ f
v
⫽ 1) cannot be achieved
within the dots even at carrier densities ten times greater than
the total number of available QD states. Figure 4 also shows
the effect that decreasing temperature has on the population
inversion. At room temperature the population inversion
saturates at ⬃0.2 to 0.3 of the maximum value, so that the
gain available is limited to ⬃20% to 30% of its maximum.
As the temperature is decreased, the Fermi function becomes
sharper and the influence of the wetting layer is reduced. The
population inversion therefore approaches the maximum
FIG. 2. Measured modal gain as a function of injection current and tem-
perature. The measurement is taken at the lasing wavelength.
FIG. 3. Estimate of the DOS for the lasers. An equivalent DOS is plotted for
the dots, where the integral area represents the total number of available
energy states.
4905Appl. Phys. Lett., Vol. 81, No. 26, 23 December 2002 Matthews
et al.
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value. The analysis confirms that the gain saturation seen in
the experimental data is consistent with the occupancy of
wetting-layer states. Population of excited dot states would
also lead to gain saturation,
9
however, for our samples the
wetting layer is dominant due to its large relative degeneracy
and the small confinement energies for carriers within the
QDs.
In summary, we have presented experimental evidence
of gain saturation in QD lasers. The results are consistent
with a calculation of the current and temperature dependence
of the inversion in the dot states when the population of
wetting-layer states is included. Thus, the dot gain can satu-
rate below its maximum value, with this saturated value in-
creasing with decreasing temperature. At room temperature
this reduces the available gain to ⬃30% of its maximum.
The gain data also indicates that at 100 K the dots are effec-
tively de-coupled from the wetting layer, and in this case
total population inversion can be achieved.
One of the authors 共D.R.M.兲 is supported by the U.K.
Engineering and Physical Sciences Research Council.
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FIG. 4. Population inversion factor plotted as a function of total carrier
density. Here, the carrier density is normalized to the total number of avail-
able dot states (N
QD
⫽ 4⫻10
10
cm
⫺ 2
).
4906 Appl. Phys. Lett., Vol. 81, No. 26, 23 December 2002 Matthews
et al.
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