Download Ultrafast carrier dynamics of resonantly excited 1.3

Physica B 314 (2002) 263–267
Ultrafast carrier dynamics of resonantly excited
1.3-mm InAs/GaAs self-assembled quantum dots
F. Quochia,*, M. Dinua, N.H. Bonadeoa, J. Shaha, L.N. Pfeifferb,
K.W. Westb, P.M. Platzmanb
a
Lucent Technologies, Bell Laboratories, 101 Crawfords Corner Road, Holmdel, NJ 07733, USA
b
Lucent Technologies, Bell Laboratories, Murray Hill, NJ 07940, USA
Abstract
We report the carrier dynamics of 1.3-mm InAs quantum dots (QDs), following resonant excitation in the lowest
energy state of QDs. The strong temperature dependence of the escape rates of the carriers leaving the ground state
shows the presence of efficient multiphonon processes, involving both acoustic and optical phonons. The very fast
activation of electrons to the first excited state implies that, in these QDs, the phonon bottleneck is not observable at
room temperature even at low carrier densities where the dynamics is independent of excitation level. r 2002 Elsevier
Science B.V. All rights reserved.
Keywords: Self-assembled quantum dots; Phonon bottleneck; Ultrafast carrier dynamics
Self-assembled InAs quantum dots (QDs) have
been extensively investigated in the last few years
(for a recent review see Ref. [1]). Three-dimensional confinement in these nanostructures profoundly modifies the intrinsic physical processes
that dominate carrier dynamics and relaxation
compared to higher dimensional systems. Due to
the discrete electronic states with large energy
separation, it has been predicted that efficient
carrier relaxation is possible only between states
whose energy difference is close to (a multiple of)
longitudinal optical phonon (LO) energy [2].
However, until very recently, the so-called phonon
bottleneck has not been observed in QDs. Many
mechanisms that circumvent the phonon bottleneck have been proposed to explain the experimental results. A very recent experiment has
*Corresponding author. Fax: +1-732-949-2473.
E-mail address: [email protected] (F. Quochi).
revealed the presence of the phonon bottleneck
in self-assembled quantum dots at low temperatures (B40 K) [3].
In this paper, we report measurements of the
depopulation dynamics of the lowest electronic
states of the quantum dots and the dynamics of the
first excited electronic states, following resonant
excitation in the lowest states by a subpicosecond
optical pulse, using differential transmission and
upconversion luminescence techniques. Photoluminescence (PL) studies are sensitive to the
product of the electron and hole occupation
functions fe fh ; while differential transmission
(DT=T) is sensitive to the sum fe þ fh ; thus
allowing distinction between thermal activation
rates for electrons and holes.
The self-assembled InAs/GaAs QDs are fabricated by molecular beam epitaxy on a GaAs
substrate [4]. Sample #1 (#2) consists of two (four)
stacks of three (two) QD layers each, designed to
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 3 8 3 - 7
F. Quochi et al. / Physica B 314 (2002) 263–267
PL
1E-5
∆T/T
τh~1 ps
1E-6
DT
τe~70 ps
0.0
0.2
(b)
0.1
1
τr~600 ps
0.4 0.6
Time [ns]
(a)
5
4
3
2
1
0
0.92 0.96 1.00
Energy [eV]
90
80
70
60
50
40
τ e(ps)
emit near 1.3 mm at room temperature. Each QD
layer consists of a seed InAs layer followed by a 6period GaAs/InAs superlattice. The QD layers
( of
within a stack are separated by 200 (4 0 0) A
( of
GaAs, and the stacks are separated by E1500 A
GaAs. From transmission electron microscopy, we
estimate a QD density ntot B324 1010 cm2 per
layer. The QDs have a base length bB30 nm and a
height hB10 nm. High-excitation PL spectra show
evidence of three electron and hole confined states
and confirm the high quality of the QDs.
The DT=T measurements are performed using
150 fs pulses from an optical parametric oscillator
(pumped by a Ti:Sapphire laser), tuned to the
lowest interband transition energy of the QDs in
the standard degenerate pump-probe configuration with orthogonally linearly polarized pump
and probe fields. The high sensitivity (B107)
required to perform low-density measurements is
achieved by combining high-frequency modulation
(0.5–1.5 MHz) and lock-in detection with balanced
detection. The lattice temperature is varied in the
range 10–400 K. Time-resolved PL data at room
temperature are obtained using a standard upconversion PL setup. The PL signal is excited by a
linearly polarized 150 fs pulse and the emission is
collected by a Cassegrain reflector, focused onto a
1-mm thick LiIO3 nonlinear crystal, upconverted
using a residual beam from the Ti:Sapphire laser,
then dispersed in a double spectrometer and
detected by a low-noise GaAs photomultiplier.
The excitation spot size (1/e2 diameter) used in the
pump-probe (PL) experiment is 70 (60) mm.
Fig. 1a depicts the room temperature resonant
DT=T dynamics of sample #1 versus pump-probe
time delay. The positive sign of the DT=T signal
indicates bleaching of absorption due to state
filling by photoexcitation. The observed recovery
of absorption results from depopulation of these
states by various processes. The right inset shows
the peak DT=T signal versus laser wavelength,
together with the nonresonantly excited cw PL
spectrum. The spectra show that the DT=T signal
arises from the lowest QD interband transition.
The temporal decay can be fitted quite well by a
three-component exponential decay (solid curve in
Fig. 1): ultrafast (th B0:8 ps), fast (te B70 ps) and
slow (tr B600 ps). The slow component has been
τh(ps)
264
0.8
Γ12
Γ21 2 e
1e
Γ20
Γ10
1h
2h
-2
n ex/n tot(10 )
1.0
(c)
WL
QD
WL
Fig. 1. (a) Resonant DT=T dynamics of sample #1 at room
temperature. The solid curve is the fit to the data of a threecomponent exponential decay. Inset: PL and DT=T spectra at
T ¼ 290 K. The laser spectral width (FWHM) is B11 nm. (b)
Hole ði ¼ h, squares) and electron ði ¼ e; dotsÞ activation rates
1=ti versus fractional occupation n of the QDs ðn ¼ nex =ntot Þ: (c)
Energy level diagram for electrons (e) and holes (h). G10 and G20
are the recombination rates. G12 and G21 are the rates between
levels 1 and 2.
studied extensively in the past (see, for instance
Ref. [5]) and is attributed to carrier recombination.
The ultrafast ð1=th Þ and the fast ð1=te Þ rates are
attributed to the activation of holes and electrons,
respectively.1 Fig. 1b shows that te and th are
independent of the pump intensity over almost two
orders of magnitude in excitation.
DT=T curves versus pump-probe delay are
measured at the resonance peak for different
lattice temperatures at the excitation intensity
Iex ¼ 25 W/cm2. Given a0 dE3:5 104 per layer
[6], we estimate a fractional (average) occupation
per dot n ¼ nex =ntot E0:0251 (regardless of spin).
The decay times te and th ; as well as their relative
amplitudes, change dramatically from 60 to 350 K.
The fits to the data reveal that te changes from
1
Since the hole levels of the QDs have smaller energy
separations than the electron levels, we assume that the holes
are activated to their QD excited states faster than the electrons.
F. Quochi et al. / Physica B 314 (2002) 263–267
E20 ps at 400 K to 400 ps at 200 K, whereas th
changes from E0.8 ps at 300 K to 20 ps at 60 K.
The dependence of the rates 1/te and 1=th on
temperature is shown in Fig. 2a and b.
We have performed model calculations on the
basis of a two-level (2+2) system for electrons and
holes (see Fig. 1c for details), assuming that the
carriers are scattered within each QD. A simple
rate equation analysis allows us to write 1=th and
1=te in terms of the intrinsic phonon rates G12 ; G21
between the two lowest QD electron and hole
levels. As is evident from Fig. 2, single LO phonon
processes cannot reproduce the temperature dependence of the escape rates; LO7LA (longitudinal acoustic) processes fail to fit the model
temperature dependence to the data as well. In
order to reproduce the steep temperature dependence we consider LO7m LA phonon processes.
Good fit to the data is obtained by using LO2LA
and LO+4LA phonon processes for 1=th and
1=te ; respectively (Fig. 2).2
Distinct distributions of dots with different
recombination rates and phonon-assisted interdot
carrier migration processes are negligible because
the relative amplitudes of the three components
are independent of wavelength across the inhomogeneously broadened spectrum. Most Augermediated activation processes can be eliminated
at these low excitation intensities because depopulation times are independent of the pump intensities (Fig. 1b), and also due to the strong
temperature dependence (Fig. 2). Electron–hole
scattering involving a single electron and a single
hole may occur within a QD [7]. In this process,
one of the carriers is excited by a different
activation process (e.g., thermal activation by
phonon absorption). The other carrier can then
be excited to a higher level by de-exciting the first
carrier to a lower level. From the point of view of
the ground-state depopulation dynamics, this
process does not seem to be very important. In
fact, if the electrons were activated by electron–
hole scattering, 1=te and 1=th would be expected
2
In the temperature range of the experiment, we can assume
that kBT>ELA, where ELA is the largest LA phonon energy
involved in the process. This allows us to have only one
adjustable fit parameter (the multiphonon rate amplitude).
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Fig. 2. Electron (a) and hole (b) activation rates 1=te and 1=th
versus inverse temperature (sample #1). The dashed, dotted and
solid curves are the best fit for a single LO, LO+LA, and
LO7m LA phonon scattering processes, respectively.
to have (almost) the same temperature dependence. In view of the above considerations and of
the fits of the rates 1/th and 1/te for different
temperatures, we infer that carriers are scattered to
higher energy states (either inside or outside the
QDs) by intrinsic multiphonon scattering processes.
To directly access the carrier dynamics in the
excited states we study the time-resolved PL signal
from the first-excited interband transition following resonant excitation in the lowest interband
transition. Since the holes are thermally activated
very rapidly, the excited-state PL signal rise time
almost corresponds to the electron activation time.
Upconversion PL measurements are performed at
room temperature in sample #2 which has 8 QD
layers and thus is more efficient. Fig. 3a shows the
PL spectrum of the QDs, upconverted 60 ps after
excitation,
for
the
excitation
intensity
Iex ¼ 1:1 kW/cm2 ðn ¼ 0:85Þ: Time-resolved PL
profiles for different Iex values are displayed in
Fig. 3b, and an exponential growth function is
fitted to the time profiles.3 The fit PL rise time
versus Iex is plotted in Fig. 3c. The numbers in
brackets are the values of n; which are derived
assuming that the optical absorption scales
3
The PL dynamics at long times is characterized by a
recombination decay time tr B600 ps (not shown).
F. Quochi et al. / Physica B 314 (2002) 263–267
2
6E-4
2
3.5
1.8
60
40
20
0.7
PL rise time (ps)
1100 1200 1300
(a) wavelength (nm)
(c)
20 (0.42)
10
0
1000
100
10
1
4E-4
∆ T/T
1.1 kW/cm
∆ t = 60 ps
7.6
PL signal (cps)
PL signal (a.u.)
Iex (kW/cm )
τi (ps)
266
τr
τe
(0.20)
0.2
2E-4
(0.90)
τh
0.4 0.6 0.8 1
2
exc. intensity (kW/cm )
0 10 20 30 40 50 60
time (ps)
(b)
0.52 kW/cm
1E-4
(0.81)
(0.41)
0
200
400
600
2
800
delay time (ps)
(0.55)
(1.0)
4
0
2
excitation intensity (kW/cm )
Fig. 3. Room temperature PL dynamics of sample #2. (a) PL
spectrum excited at the lowest QD transition wavelength
(1270 nm), upconverted 60 ps after excitation. (b) PL time
traces at the first-excited QD transition wavelength (1170 nm)
for different excitation intensity ðIex Þ values. Solid lines are
exponential growth fits to the data. (c) PL rise time versus Iex :
The numbers in brackets represent the fractional occupation
per dot, n: The dashed lines are guides to the eye.
linearly with Iex : The arrows marks the excitation
power for which n ¼ 1:4 The PL rise time increases
with decreasing Iex ; and for Iex o1 kW/cm2
ðno0:8Þ tends to a constant value of about 14 ps.
Since thermal relaxation is always faster than
thermal activation, this result qualitatively suggests that the phonon bottleneck is always
circumvented even at low carrier densities where
carrier dynamics is intensity independent.
The activation dynamics to the first excited state
with a characteristic time of 14 ps is in contrast
with the ground-state depopulation dynamics
observed in sample #1. To check the overall
consistency of our experimental results, we performed room temperature resonant DT=T measurements on sample #2 also, in the same
excitation regime as for the PL measurements
ðno1Þ: The results are qualitatively in agreement
with those obtained in sample #1: a threecomponent exponential decay fit to the DT=T
traces gives th B0:8 ps, te B120 ps, and tr B900 ps
4
We remark that in our case of resonant excitation in the
lower QD interband transition, the linear extrapolation always
overestimates the actual value of n due to absorption saturation
by state filling.
Fig. 4. Resonant DT=T dynamics of sample #2 at room
temperature for Iex ¼ 0:52 kW/cm2: Experimental data (dots),
three-component exponential decay fit to the data (solid line).
Inset: Fit decay times ti (i=h, e, r) versus Iex : Numbers in
brackets are same as in Fig. 3c.
(see main panel of Fig. 4). The recombination time
tr ; which is longer in sample #2 than in sample #1,
in fact agrees with the PL decay time in the ground
state (not shown). The inset shows that th ; te ; tr
are independent of Iex in the regime of interest
ðno1Þ; which is consistent with the constancy of
the PL rise time for no1:
The comparison between the PL and the DT=T
data suggests that thermally activated electrons
can reach various final states. Since a decay with a
characteristic time of 14 ps is not clearly identifiable in the DT=T traces, we infer that most
electrons leaving the ground state are scattered
to either highly excited states of the QDs or the
wetting layer, or defect states surrounding the
QDs. Additional investigations are required to
fully understand the carrier dynamics.
In summary, we report carrier dynamics of 1.3mm InAs/GaAs QDs studied by subpicosecond
pump-probe and photoluminescence spectroscopy
with resonant excitation in the lowest QD interband
optical transition. We observe very fast electron
activation times from which we deduce that the
phonon bottleneck is not observable at room
temperature even at low carrier densities where
the dynamics is independent of excitation level.
References
[1] D. Bimberg, M. Grundmann, N.N. Ledentsov, in: Quantum
Dot Heterostructures, Wiley, London, 1999.
F. Quochi et al. / Physica B 314 (2002) 263–267
[2] U. Bockelmann, Phys. Rev. B 48 (1993) 17637.
[3] J. Urayama, et al., Phys. Rev. Lett. 86 (2001) 4930.
[4] J. Bloch, et al., Appl. Phys. Lett. 77 (2000) 2545.
[5] M. Paillard, et al., Appl. Phys. Lett. 76 (2000) 76.
[6] D. Birkedal, et al., Appl. Phys. Lett. 77 (2000) 2201.
[7] T.S. Sosnowski, et al., Phys. Rev. B 57 (1998) R9423.
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