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Blom, C.W.P.M.

Haverkort, J.E.M.

Leys, M.R.

Mols, R.F.

Wolter, J.H.

English

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PICOSECOND CARRIER CAPTURE BY A SEPARATE CONFINEMENT
LASER STRUCTURE
P.W.M. Blom, R.F. Mols, J.E.M. Haverkort, M.R. Leys and J.H. Wolter
Department of Physics, Eindhoven University of Technology, P.O. Box 513,
5600 MB Eindhoven, The Netherlands
Abstract
The carrier capture time in a separate confinement laser structure has been studied
both experimentally and theoretically. From experiment we deduce a local capture
time (1.3 ps) which is for the first time in agreement with theory (1.2 ps).
Introduction
The capture of photoexcited carriers in semiconductor quantum well structures has
received considerable interest in both fundamental and device oriented research. For
quantum well lasers, the collection efficiency for carriers is important for both the
efficiency and the maximum attainable modulation frequency. From quantum
mechanical calculations Brum and Bastard1 predicted strong resonances in the
carrier capture time as a function of well width which have not been observed
experimentally. Moreover, the capture times found in recent experiments2-4 are
much shorter (0.3 ps - 260 ps) then predicted in ref. 1 (7 ps - 1 ns). So there seems to
be a large discrepancy between the theory and the experimental results in
literature.
In the present paper we present an ambipolar model for carrier capture. Within this
model for the first time the quantum mechanical ‘overall’ capture time (8 ps) is in
agreement with the experimental result of 10 ps. The experimental results were
obtained from subpicosecond luminescense spectroscopy on a 70 Å GaAs-AlGaAs
separate confinement heterostructure quantum well. Moreover, we are the first to
deduce a local carrier capture time of 1.3 ps from our luminescence risetime
measurements which is again in agreement with the classically defined ‘local’ carrier
capture time of 1.2 ps calculated for our structure.
Carrier capture into a quantum well
A: Classical model
The temporal development of the carrier density in a separate confinement laser
structure can be described in a one-dimensional rate equation
ECOC ‘90 - 59
¶n(z,t) ¶2n(z,t) n(z,t) n(z,t)  ,
——— = D · ——— - B · ——— - W · ———
¶z ¶z2 tb tc
where z is the direction perpendicular to the quantum well layer. In this equation D
is the ambipolar diffusion constant, B and W are unity in the barrier and well,
respectively, and zero elsewhere. The recombination losses in the barrier are given
by tb-1 and the scattering rate of carriers into the well is determined by a local
capture time tc-1. The capture time is called local because in this model capture is
only possible when a carrier is above the well. After capture into the well the
relaxation and radiative recombination of the carriers are described by simple rate
equations. It is important to note that the calculations are performed under
ambipolar conditions, the strong interactions between electrons and holes maintain
an equal distribution of electrons and holes in the structure. The relaxation time
constant within the well and the radiative lifetime of the carriers can be determined
by direct excitation (below the barrier bandgap) into the well. The diffusion
constant and the local capture time are then provided by indirect excitation (above
the barrier bandgap).
B: Quantum mechanical model
We consider a GaAs quantum well of width L between two AlxGa1-xAs barriers, the
total barrier width Ls is 1000 Å. The probability that a carrier emits a LO phonon
and becomes captured by the well is calculated using Fermi’s Golden rule. It is
assumed that no LO phonons are present, so there is no thermally activated escape
from the well. Using Froehlich’s Hamiltonian the capture probability is given by
2p S S ò dq^ |Hfi|2 d(Ei(k,k^)-Ef(n,k,k^)-£wph) ,
t-1 = —  q  n
£
with q and k the phonon and electron wavevector parallel to the quantum well layer
and n numbers the subbands in the well. The capture time t is now valid for
carriers in the whole structure and is therefore called the overall capture time. It is
important to note that the overall capture time still contains a diffusion time in the
AlGaAs barrier and is thus a function of barrier thickness. These calculations were
first presented by Brum and Bastard1 for a barrier thickness of 1 mm. The capture
times of the electrons and holes were calculated separately and show strong
oscillations as a function of well width. If we want to compare their theoretical
predictions with our classical diffusion model, in which an ambipolar carrier
distribution is assumed, an ambipolar capture rate has to be determined. This can
be achieved by coupling the electrons and hole capture rates in a rate equation,
ECOC ‘90 - 60
dn n 1  p n (te + th) n  ,
–– = - — - –(— - —) = - ———– · n = - —
dt te 2  th te 2t e th ta
dp p 1  p n (te + th) p   ,
–– = - — + –(— - —) = - ———– · p = - —
dt th 2  th te 2t e th ta
where te,th are the overall capture times for the electrons and the holes
respectively. The ambipolar overall capture time ta is shown in fig.1 as a function of
well width.
By equating the calculated quantum mechanical capture rate to the classical
capture rate, we obtain the local capture time as a function of well width.
FIG.1.Calculated ambipolar overall
capture time vs well width L [Å].
FIG.2.Calculated ambipolar local
capture time vs well width L [Å].
The local capture time is shown in fig.2 as a function of well width for a barrier
thickness of 1000 Å. We find that the oscillations of the quantum mechanical
overall capture time (2-30 ps) give rise to oscillations (0.2-0.6 ps) of the local
capture time.
Experimental results
We report direct measurements of the carrier capture times in a MBE-grown
GaAs-AlGaAs laser structure by subpicosecond luminescence spectroscopy using an
upconversion lightgate. The conduction band of the laser structure is shown in fig.3.
The time evolution of the well luminescence after direct and indirect excitation with
a subpicosecond laserpuls (0.6 ps) is shown in fig.4.
From these results an overall capture time of 10 ps is deduced, which is in good
agreement with the calculated ambipolar capture time of 8 ps (see fig. 1). By
applying the diffusion model we obtain a local capture time of 1.3 ps. When our
model is extended to a structure with 3 quantum wells, the theoretical local capture
ECOC ‘90 - 61
time is rising from 0.6 ps (see fig.2) to 1.2 ps, which is in excellent agreement with
the experimentally observed value of 1.3 ps. With our ambipolar model we are now
able to investigate the dependence of the overall and local capture time on the well
width. From our calculations a change in well width from 70 Å to 50 Å yields a
decrease of the local capture time by a factor 2.
FIG.3. Conduction band structure of
separate confinement laser structure.
FIG.4. Time dependence of well
luminescence for an excitation.
density of 5· 1017 cm-3, T=7.0 K
Conclusions
In conclusion we show that the carrier capture in a separate confinement laser
structure is well described by an ambipolar capture model. From subpicosecond
luminescence spectroscopy experiments on a 70 Å quantum well an overall capture
time of 10 ps is derived, which gives rise to a local capture time of 1.3 ps. The
spreading of the capture times reported in literature is mainly due to a mixing up of
overall and local capture times.
1 J.A. Brum and G. Bastard, Phys.Rev. B 33, 1420 (1986)
2 E.O. Göbel, H. Jung, J. Kuhl and K. Ploog, Phys.Rev.Lett. 51, 1588 (1983)
3 B. Deveaud, J. Shah, T.C. Damen and W.T. Tsang,
Appl.Phys.Lett. 52, 1886 (1988)
4 B. Deveaud, F. Clerot, A. Regreny, K Fujiwara, K. Mitsunaga and J. Ohta,
Appl.Phys.Lett. 55, 2646 (1989)
ECOC ‘90 - 62
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PICOSECOND CARRIER CAPTURE BY A SEPARATE CONFINEMENT LASER STRUCTURE

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