Download Carrier capture times in 1.5 - Technion

Carrier capture
times in 1.5 pm -multiple quantum
well optical
amplifiers
S. Weisqa) J. M. Wiesenfeld, D. S. Chemla,a) G. Raybon, G. Sucha,a) M. We ener,b)
G. Eisenstein ‘) C. A. Burrus, A. G. Dentai, U. Koren, B. I. Miller, H. Temkin, #
R. A. Logan,dj and T. Tanbun-Ekd)
AT&T Bell Laboratories, Holmdel, New Jersey 07733
(Received 19 August 1991; accepted for publication 21 October 1991)
The carrier capture times in multiple quantum well semiconductor amplifiers of different
structures are studied under high plasma density conditions. Fast ( < 1 ps), slow ( > 150 ps),
and intermediate time constants (2-7 ps) are identified in InGaAs qtiantum well
structures. The intermediate time constant is attributed to carrier diffusion in the cladding
layers and identified as the carrier capture time. Short capture times can be achieved
by proper design of the device structire.
The capture times of carriers into quantum wells
(QW) have been the subject of several studies in the last
few years. These studies are motivated by both practical
and fundamental reasons. It was suggested, only recently,
that the capture time into the QWs is directly related to the
nonlinear gain compression observed in these lasers.’ The
nonlinear gain compression factor E is a phenomenological
parameter that is inserted in the rate equations model of
the laser to explain the nonlinearity of its gain. While the
physics behind E is far from understood, it has been found
that by introducing this parameter one can model quite
well the damping behavior of lasers at high frequencies.”
For bulk lasers, it was suggested that spectral hole
burning3 and/or carrier heating’ are the mechanisms underlying nonlinear gain compression. For QW lasers, however, the magnitude of E is often larger than for bulk lasers
and therefore cannot be explained solely by the above
mechanisms.’ An additional mechanism, related to the carrier capture time in the QW, may explain the observed
increase in E for QW lasers.
The capture process has been studied experimentally
by photoluminescence, photoluminescence excitation,5 and
time-resolved luminescence6 spectroscopies on specially
designed QW structures, where the carriers were introduced into the sample by optical excitation. The theoretical
efforts that followed these experiments took two different
approaches. The semiclassical approach’ shows that the
capture efficiency decreases when the QW width becomes
smaller than the optical phonon limited mean-free path.
More elaborate quantum mechanical approaches,8 which
calculate the scattering rates into the QWs by taking into
account the longitudinal optical (LO) phonon coupling
into the final QW states, predict strong oscillations in the
capture time as a function of the well width. The singleparticle picture, however, cannot account for the manybody effects in a real, active laser structure and, in particular, does not consider the effects of carrier-carrier
scattering. Our experiments are designed to study carrier
capture in active laser devices in exactly that regime, by
@Present address: Lawrence Berkeley Laboratory, Berkeley, CA 94720.
b)Present address: Fachbereich Physik, Universitat Dortmund, Dortmud, Germany.
‘)Present address: Dept. of Elect. Eng., Trchnion, Haifa 32000, Israel.
d)Presentaddress:AT&T Bell Laboratories,Murray Hill, NJ 07974.
9
measuring gain recovery dynamics subsequent to gain
compression caused by an intense, ultrashort optical pulse.
We investigated six samples with different geometries.
In Fig. 1 we show the band gap structures of the samples.
The first four MOCVD-grown samples (samples 1 to 4),
Fig. 1 (a), are separate confinement heterostructures, consisting of a few (four for samples 1, 3, and 4, three for
sample 2) In,Ga, _ ,& QVys, separated by InGaAsP barrier layers with a 0.95 eV band gap (il,, = 1.3 pm). On
both sides of the multiple QW structure are InGaAsP cladding layers with the same composition as the barriers.
These cladding layers define the optical waveguide and
store the carriers. For the latter reason, we henceforth call
them the “reservoir” (RES) . The contact layers consist of
InP. The QWs of samples 2 and 3 are compressively
strained (X = 0.77), whereas those of samples 1 and 4 are
unstrained (x = 0.53). The widths of the QW, the barriers
and the RES are listed in Table I. The transition from the
/I RI%= 1.3 pm layers to the InP layers was either with a
single step, Fig. 1 (a), or a few discrete steps [not shown in
Fig. 1 (a)]. We also had one graded gap (and index) sample which was compressively strained (x=0.66),
5 and
Fig. 1 (b), and a control sample, with no QWs (conv&ntional LPE-grown V-groove laser’), 6 and Fig. 1 (c) . Highquality antireflection SiO, coatings (reflectivity < 10 - 3,
were deposited on both facets of the samples to make optical amplifiers. With these coatings it is possible to inject a
very high current density with no clamping of the population inversion. This was experimentally verified by measuring the spectrum of the amplified spontaneous emission of
the processed samples.” From these measurements we estimate a carrier density in the QWs close to or in excess of
1019 cm ~ 3 under high current injection ( -200-300 mA
for .- 500 pm-long devices). That high density implies that
the average distance between carriers is -50 A, i.e., ( the
Bohr radius of the excitons in the QWs.
The gain recovery dynamics were measured by a
pump-probe technique, using 0.4 ps duration pulses from
an additive pulse modelocked (APM) color center laser,”
operating at 76 MHz repetition rate. The pump pulse was
polarized perpendicular to the junction plane of the amplifier (TM polarization) and orthogonal to the probe pulse
(TE polarization). With this arrangement of beam polarizations, the test beam probes the TE gain dynamics.”
Appl. Phys. Lett. 60 (I), 6 January 1992
0003-6951/92/010009-03$03.00
@ 1992 American Institute of Physics
9
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sample
#6
I
time (ps)
FIG. 2. Typical time resolved gain recovery spectra for the control sample
6, for sample 1, and for sample 3.
InGaAsP
(1.55
pm)
FIG. 1. The band gap structure of the semiconductor amplifiers used in
the experiment. The QW samples l-4 (a), the graded index sample 5(b)
and the control sample 6(c), which has no QWs but an InGaAsP active
layer.
Pump and probe beams were combined in a fiber directional coupler and coupled into the amplifier using a fiber
with a microlens. The pump pulse energy at the amplifier
input was 4 pJ or less, producing up to 8 dB of gain compression, and was at least 100 times more intense than the
probe.
The pump pulse removes carriers form the bottom of
the QWs, primarily by stimulated emission, but also by free
carrier absorption. The recovery of the gain is then monitored by the probe pulse. In principle, one should distinguish the following sequence in the carrier dynamics: Immediately after the removal of the carriers,” the remaining
population of carriers in the QWs is nonthermal. Those
carriers first thermalize among themselves (hole burning
.- 10-100 fs). Then, they thermalize with the lattice (carps). Recently, an intermediate time
rier cooling -0.7-l
constant ( - 250 fs) was measured and attributed to carrier
heating and/or hole burning.” Next, as has been shown in
previous work,” the carriers from the RES replenish those
that were removed from the QW by the pump on a 2-10 ps
time scale. Finally, carriers from the contacts reestablish
the steady-state population, on a time scale of few hunTABLE I. Summary of the samples’ parameters and dimensions.
Total
I
1
2
3
4
5
6
2620
2655
1570
1535
800a
2400b
2000
2400
1200
500
2200
2400b
I
yrj”
yr;
80(x4)
25(x3)
25(X4)
90(X4)
30(X4)
2400b
100(X3)
90(X2)
90(X3)
225(X3)
225(x3)
...
Strain
(46)
Carrier
capture time
(PS)
no
yes(1.53%)
yes(1.53%)
ye$:3%)
IlO
‘At the bottom of the RES.
‘For this sample, the active layer thickness = total clad = la,.
10
Appl. Phys. Lett.. Vol. 60, No. 1, 6 January 1992
7
4.5
2
4
14
0
dreds of picoseconds, limited by Auger recombination.”
Typical time-resolved gain measurements, taken on
three different devices, are shown in Fig. 2. We plot gain
compression, in dB, as a function of the time delay between
the pump and the probe. Both the strained and the nonstrained samples were showing the same qualitative dynamics. The three traces are arbitrarily displaced on the
vertical axis, for clarity. The upper trace (device 6), taken
on the bulk amplifier, shows only a fast recovery (attributed to carrier cooling1”‘3), on the order of 1 ps, and a
very slow recovery ( 170 ps), hardly resolved in Fig. 2,
which is Auger recombination limited. The center and the
lower traces, taken on devices 1 and 3, respectively, show,
in addition to fast ( < 1 ps) and slow ( > 150 ps) time
constants, an intermediate time constant, which we attribute to carrier diffusion in the reservoir. This intermediate time constant, which we identify as the carrier capture time, has values of 7 and 2 ps for the curves shown for
devices 1 and 3, respectively. Values of the intermediate
time constant for all the devices are plotted in Fig. 3 as a
function of the square of the reservoir width lREs based on
20
.,.,.I.I.I.I.I.I.I.
18
16
14
-2
;
x
F
p
cc
12
10
6
4
2
0
0
2
4
6
8
10
(l~27T)2(a"gstrom5
12
14
16
18
20
x 10'
FIG. 3. Capture time, for all six devices under study, as function of the
square of the reservoir width &s. The horizontal error bars for samples
S and 6 represent the uncertainty in these values.
Weiss et al.
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10
the predictions of our model.14 The data points shown are
the averages of many independent measurements of the
time constants for different values of amplifier bias, pump
intensity, and pump wavelength. As long as the bias of the
amplifier is sufficiently high to place the Fermi level in the
RES, the measured time constants are independent of the
above parameters.
The carrier capture process includes carrier transport
in the RES and inelastic scattering from the RES to the
QW. The latter process is referred to as a “local capture
time,” while the sum of all processes is the “overall capture
time.” The theory used to calculate the quantum mechanical capture time assumes that electrons and holes are in
coherent states in the QW and the RES, and it uses the
Fermi golden rule to calculate the transition rate between
the RES and QW states caused by various coupling mechanisms, such as the emission of LO-phonons. The predicted oscillations in the capture times originate essentially
from corresponding oscillations in the wave function overlap. This procedure may be legitimate at vanishingly small
densities, i.e., when the photocarriers have the possibility
of establishing coherent wave functions. We argue that, at
the very large densities encountered in laser amplifiers,
carrier-carrier scattering induces such a lifetime broadening of the quantum states that, for RES large enough, the
carriers, and especially those at the bottom of the RES, can
be treated as a classical fluid.14 Thus, their dynamics is
better described in terms of diffusion. The reservoir states
are rapidly depopulated locally above the QWs by the
emission of LO phonons, but are repopulated almost instantly due to elastic and inelastic scattering processes.
Therefore, the overall capture time will be limited by the
macroscopic transport properties of the carriers in the
RES, namely, diffusion. I5
We modeled the gain recovery dynamics, assuming
that the rate limiting step is diffusion. Thus, the relevant
time constant is the time required to till in a “hole” created
at time zero at the center of a distribution of classical
carriers, which occupies a region of width IRES.This time
constant was calculated applying standard diffusion
theory.14V16The model predicts that the capture time depends on the reservoir width, as 71) = (&/27r)
2/D, where
D is the ambipolar diffusion constant. The fit to this model
is shown in Fig. 3, where the first four samples ( 1 to 4) fall
on the same line, whose slope gives D=2.9 cm2/s; this
value is in good agreement with the ambipolar diffusion
constant for 1nGaAsP.t’ The bulk sample (6)) of course,
does not show up on the line, since there is no vertical
transport or diffusion involved in this sample. A surprising
result, however, is the measured capture time for the
graded index sample (5). The common belief is that carrier
capture in this structure is faster than in nongraded struo
tures and, indeed, there are some experimental data that
support this belief.6 The reason for the slower capture time
for our graded index sample is not clear, and more systematic study needs to be done. We propose, nonetheless, a
possible explanation. The local (quantum mechanical)
capture time will show up as the dominant capture time
only when the carriers can establish a coherent quantum
11
state in the RES. Such will be the case when either collisions are rare (low density) or the width of the RES is
small (the reservoir dimensions are comparable to those of
the QW>.14 The latter case occurs for the graded index
sample, because ZREsat the bottom of the reservoir is only
800 A. It is possible that the slow time constant measured
for this sample is related to the quantum mechanical oscillations in the capture time.’
In summary, we have shown that the capture time into
the QWs is, under normal operating conditions, diffusion
limited. To obtain the shortest possible capture time (and
the smallest nonlinear gain compression factor) in high
speed lasers, the design of the structure must take into
account both diffusion and quantum mechanical considerations. The experimental results demonstrate, however,
that rapid gain recovery can be engineered into the device
structure.
We would like to acknowledge D. W. Taylor for his
technical help with the data acquisition software. During
this work S. Weiss was partially supported by the Rothschild fellowship.
’W. Sharfin, J. Schlafer, W. Rideout, B. Elman, E. Koteles, R. B. Lauer,
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il
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