Tunneling carrier escape from InAs self-assembled quantum dots
J. Ibáñez, R. Leon, D. T. Vu, S. Chaparro, S. R. Johnson, C. Navarro, and Y. H. Zhang
Citation: Applied Physics Letters 79, 2013 (2001); doi: 10.1063/1.1402642
View online: http://dx.doi.org/10.1063/1.1402642
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APPLIED PHYSICS LETTERS

VOLUME 79, NUMBER 13

24 SEPTEMBER 2001

Tunneling carrier escape from InAs self-assembled quantum dots
J. Ibáñez,a) R. Leon, and D. T. Vu
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena,
California 91109

S. Chaparro, S. R. Johnson, C. Navarro, and Y. H. Zhang
Center for Solid State Electronic Research, Arizona State University, Tempe, Arizona 85287

共Received 20 April 2001; accepted for publication 13 July 2001兲
Deep-level transient spectroscopy measurements in InAs quantum dots 共QDs兲 grown in both
n-GaAs and p-GaAs show that tunneling is an important mechanism of carrier escape from the dots.
The doping level in the barrier strongly affects the tunneling emission rates, enabling or preventing
the detection of a transient capacitance signal from a given QD level. The relative intensity of this
signal acquired with different rate windows allows the estimation of tunneling emission energies.
© 2001 American Institute of Physics. 关DOI: 10.1063/1.1402642兴

Stranski–Krastanow quantum dots 共QDs兲 have recently
attracted much attention due to their unique optical and electronic properties, which are enabling a wide range of novel
applications.1 The transition energies between QD electron
and hole levels can be directly measured from photoluminescence 共PL兲 peaks. However, PL provides little information
on electron and hole levels relative to the barrier band edges.
Space charge techniques such as capacitance–voltage spectroscopy (C – V) 2–5 and deep-level transient spectroscopy
共DLTS兲6 –9 allow absolute positioning of the QD levels, providing complementary information to PL. Carrier capture
and escape dynamics of the dots can also be studied by
means of DLTS. There has been some discrepancy between
different published works on DLTS in the extensively studied InAs/GaAs self-assembled QDs. Direct measurements of
the energy difference between the dot levels and the energy
band of the barrier7 have been reported, while other works
show evidence of capture barriers into the dots.8 The possibility that some of the DLTS signals detected are originated
from traps near the dots has also been suggested.9 To this
day, only one study has reported clear detection of electron
escape by means of tunneling in InAs QDs.7 In the present
work, DLTS measurements performed on InAs QDs embedded in n- and p-GaAs show that tunneling is an important
escape mechanism in quantum dots. Tunneling emission
rates and energies are estimated by means of C – V and
DLTS.
QD structures were grown by molecular beam epitaxy.
Two samples with eight 50-nm layers of n-type 共p-type兲
GaAs (n⫽p⫽1017 cm⫺3) terminated with InAs QDs
共⬃2 ML coverage兲 were grown over a 300-nm-thick,
n ⫹ -doped GaAs buffer layer. A final GaAs capping layer
with the same doping level was deposited. A top Schottky
diode and back ohmic contacts were formed for the n-type
sample, and back and top ohmic contacts were formed on the
p-type sample. The DLTS measurements were carried out at
delay times ␶ in the 共0.02–1000兲 ms range and at a rate
window10 of 4.3⫻ ␶ .
Analysis of island sizes and densities using atomic force
Present address: Institut Jaume Almera 共C.S.I.C.兲, Barcelona, Spain.

a兲

microscopy in air give average diameters of 40 nm, 5 nm
heights, and concentrations of 3⫻1010 cm⫺2 for uncapped
QDs grown under the same conditions. PL spectra for these
structures were obtained at 300 and 77 K using an Ar⫹ laser
for excitation and a cooled Ge detector with lock-in techniques for signal detection. The extrapolated ground state
emission at 4 K is ⬃1.15 eV, with full width at half maximum ⬃130 meV.
A typical C – V profile obtained at 75 K for the n-type
sample is shown in curve A 共filled circles兲 of Fig. 1. Three
plateaus corresponding to three different layers of dots are
observed in addition to the background capacitance from the
doped GaAs layers. Since only one plateau per QD level is
expected,2 we attribute each plateau to the emptying of a
single QD level. Curve C 共filled circles兲 of Fig. 1 shows a
similar behavior for the p-type sample. High leakage current
for this sample allows biasing only to 2 V, therefore, only
two plateaus were observed.
Models of different level of sophistication have been
used to study the C – V profile of single QD layers.3,5 A simpler analysis of the C – V profile is possible by calculating
the charge in the dots as a function of the applied voltage by
using the expression reported in Refs. 3–5 for the density of
electron states in the QD sheet but assuming that the

FIG. 1. Capacitance–voltage profile at 75 K for n-InAs QDs 共curve A, filled
circles兲 and p-InAs QDs 共curve C, filled circles兲. Calculated C – V profiles
are shown as solid curves. Curve B shows DLTS-signal intensity vs reverse
bias at 20 K for the n-type sample. The dashed line is a guide to the eye.

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2014

Ihár̃ez et al.

Appl. Phys. Lett., Vol. 79, No. 13, 24 September 2001

FIG. 2. DLTS spectrum ( ␶ ⫽0.02 ms) for the n-type InAs-QD sample 共open
circles兲, for biasing conditions ⫺0.75 V/⫺0.05 V, and for the p-type InAs
QDs 共filled circles兲, for biasing conditions ⫺0.75 V/⫺0.05 V ( ␶ ⫽5 ms).
The inset shows the intensity of the flat signal at 20 K for the n-type 共open
circles兲 and the p-type samples 共filled circles兲 vs delay time.

depletion-region approximation still holds. The total capacitance is then given by the QD-related capacitance plus the
background capacitance. This method, already applied using
a lever-arm relation for a single layer of dots in Ref. 4, facilitates the calculation for a multilayered system. Within this
approach we obtain the best fit 共solid line兲 to curve A of Fig.
1 when one QD level with energy E n ⫽250 meV below the
GaAs conduction band and energy dispersion ⌬E n
⫽140 meV is taken into account. For the p-type sample we
obtain the best fit 共solid line兲 to curve C with one single QD
level with energy E p ⫽110 meV above the GaAs valence
band and energy dispersion ⌬E p ⫽140 meV.
Figure 2 共open circles兲 shows a DLTS spectrum for the
n-type sample, consisting of a quasiflat signal that extends
over the whole range of temperatures. A DLTS peak 共not
shown in the graph for scaling reasons兲 with an activation
energy of 0.40 eV appears for higher temperatures. Since this
peak was only detected for positive or low negative filling
biases, we believe it to be related to deep surface traps and
not to the dots. The spectrum for the p-type sample 共filled
circles兲 shows a flat signal for the lower temperatures, and a
step-like reduction to zero signal at about 55 K. To understand both spectra we must take into account that two carrierescape mechanisms exist: thermal escape and tunneling. In
the former, the quantum dot behaves like a deep trap and
hence its thermal emission rate e th is given by e th
⫽AT 2 exp(⫺Ea /KT), where E a is the activation energy of the
QD level and A is a temperature-independent constant proportional to the capture cross section.10 On the other hand,
assuming a triangular barrier for the carriers trapped in the
QDs, the tunneling escape rate can be written as11

intensity of this signal depends on the tunneling emission
rate and the rate window. For sufficiently high temperatures,
thermal emission dominates, giving rise to a step-like reduction of the tunneling flat signal at the temperature of the
DLTS peak that would be present in the absence of carrier
escape by tunneling. This allows estimating the activation
energy of QD levels by Arrhenius plots, determining the position of the step for different rate windows. The lowtemperature flat signal obtained for the p-type sample originates by hole tunneling escape from the dots, whereas the
reduction to zero signal at about 55 K arises from thermal
escape. We obtain a value of 100⫾20 meV for the activation
energy of the QD hole level, which is in good agreement
with the C – V results. Slight variations of this value are obtained depending on the applied reverse bias, which can be
explained by variations of the energy level of the dots due to
the electric field. No step-like reduction is detected for the
n-type sample 共open circles in Fig. 2兲 up to 325 K because
the DLTS signal detected at higher temperatures hinders any
other feature. The inset of Fig. 2 plots the intensity of the flat
signal at 20 K for both the n-type and the p-type samples as
a function of the delay time. For the n-type sample, the flat
signal is detected with the lowest rate window available 共delay time of 0.02 ms兲. For the next wider rate windows 共delay
times of 0.05 and 0.1 ms兲 the flat signal detected is strongly
reduced, which is a consequence of high rate of electron
escape by tunneling. For the next rate windows available, no
signal at all is detected. To further confirm that the flat signal
obtained for the n-type sample is originated by electrons
escaping from the dots, we have measured its intensity at 20
K versus applied reverse bias. A positive filling bias was
used to include the first layer of dots. The result, plotted in
Fig. 1 共curve B兲, shows three plateaus that coincide with the
plateaus of the C – V measurement 共curve A兲. The intensity
of the flat signal increases when the applied reverse bias is
sufficient to include a given layer of dots. For higher reverse
bias the tunneling escape rate increases due to the increase of
the electric field, and this diminishes the intensity of the flat
signal.
For a carrier captured in a QD level to escape, the level
must be above the Fermi energy in the barrier region. This
happens for a certain onset reverse bias V c that, within the
depletion approximation, satisfies the relation ⫺q ␺ (V c )
⫹E h ⫽q(V c ⫹ ␺ 0 )⫺E F , which leads to

冉 冊

E h ⫺q 共 V c ⫹ ␺ 0 兲 1⫺

L
W

2

⫹E F ⫽0,

共2兲

where ␺ (V c ) is the potential at the dot layer, E F is the Fermi
energy at the barrier, W⫽ 关 2( ␺ 0 ⫹V c ) ⑀⑀ 0 /qN A,D 兴 1/2 is the
depletion-region width, L is the distance from the dots to the
diode junction, N A,D is the doping level at the barrier and ␺ 0
is the built-in potential. For this voltage V c , the electric field
qF
4 共 2m * 兲 1/2E 3/2
h
F at the dots can be calculated using the depletion approxie tun⫽
,
共1兲
1/2 exp ⫺
4 共 2m * E h 兲
3
qបF
mation. By inserting the value of F into Eq. 共1兲, the lowest
where E h is the barrier height, F is the electric field at the
emission energy that gives rise to tunneling rates detectable
dot, q is the electron charge, and m * is the effective mass of
with the shortest rate window available 共delay time of 0.02
the carriers in the energy band of the barrier material. For
ms兲 can be calculated. A lower emission energy would yield
sufficiently low temperatures, the total emission rate e n
carrier escape rates too fast to be detected with our instru⫽e th⫹e tun is dominated by tunneling, which is temperature
mentation. We calculate that our lowest experimentally deThis article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
independent and therefore yields a flat DLTS signal. The
tectable emission energy is about 0.17 eV for electrons,

冉

冊

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Ihár̃ez et al.

Appl. Phys. Lett., Vol. 79, No. 13, 24 September 2001
TABLE I. QD energy level obtained by C – V measurements 共first column兲,
compared with activation energy E a 共second column兲 and barrier height E h
共third column兲 obtained from DLTS.

InAs/n-GaAs QDs
InAs/p-GaAs QDs

E n,p

Ea

Eh

0.25 eV
0.11 eV

¯
0.10 eV

0.27 eV
0.13 eV

about 0.15 eV for light holes, and about 0.060 eV for heavy
* ⫽0.076 and
holes. We have used the values m e* ⫽0.068, m lh
* ⫽0.50 for the effective mass of the different carriers.12
m hh
Hence, the doping level in the n-type barrier does not allow
detection of DLTS signals from shallower QD electron levels
共higher-energy excited states measured by PL兲. For the
p-type sample, we attribute the DLTS signal obtained to tunneling from a heavy hole level, since its emission energy is
of about 0.10 eV, whereas no light hole levels lower than
0.15 eV can be observed for the experimental conditions of
this work. Different results reported in the literature on InAs
QDs could be accounted for by different doping levels in the
GaAs matrix. Additional investigation on samples with different doping levels should be performed.
Finally, it is possible to evaluate the tunneling emission
energy by measuring the relative intensity of the tunnelingrelated flat signal of two different DLTS spectra acquired
with two different rate windows, defined by the time intervals (t 1 ,t 2 ) and (t 1⬘ ,t 2⬘ ), respectively.10 The relative intensity
of these tunneling signals is given by
exp共 ⫺e tunt 2 兲 ⫺exp共 ⫺e tunt 1 兲
I
⫽
.
I ⬘ exp共 ⫺e tunt 2⬘ 兲 ⫺exp共 ⫺e tunt ⬘1 兲

2015

the energy values that we calculate would be average values
of the QD levels involved. Whereas C – V provides information about discharging of the QD levels with respect to the
position of the Fermi energy, DLTS provides information
about the barrier that the carriers must overcome to escape. It
should be noted that the sum of the hole and electron energy
levels determined with C – V and DLTS plus the ground-state
recombination energy for the dots studied in this work 1.15
eV at 4 K兲 is close to the GaAs band gap 1.52 eV at 4 K兲.
This fact and the closeness of the QD-level energies obtained
by C – V and DLTS do not support the concept of capture
barriers for the carriers into these QDs. This is in agreement
with previous results on temperature-dependent PL14 and
time-resolved PL experiments,15 in which important capture
barriers have only been identified in low-density QDs, but
not in high-density QDs like those studied here.
In conclusion, DLTS signals detected from InAs QDs are
strongly affected by carrier escape by tunneling, with escape
rates strongly dependent on the doping density of the barrier.
The tunneling emission energies do not support the existence
of high capture barriers into these QDs.
The authors thank Salvador Dueñas for providing calibration samples, and Ken Evans for valuable experimental
input. This work was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract
with the National Aeronautics and Space Administration.
One of the authors 共J.I.兲 acknowledges the Spanish Ministerio de Educación y Cultura for financial support.

共3兲

The emission energy can then be evaluated by using Eq. 共1兲
with the value of e tun obtained from Eq. 共3兲. With this procedure, and using the data for the n-type sample plotted in
the inset of Fig. 2, we estimate tunneling emission times for
the n-type sample in the 共20–50兲 ␮s range, which leads to an
emission energy of 0.27⫾0.04 eV which is close to the value
obtained by C – V. For the p-type sample, we estimate tunneling times between 共30 and 500兲 ␮s, which gives rise to an
emission energy of 0.13⫾0.03 eV, again, close to the value
obtained with the C – V analysis. This value is also close to
the value 0.10⫾0.02 eV obtained for the activation energy
using the position of the step-like reduction in the spectra of
the p-type sample. Table I displays the different energy values for the electron 共hole兲 levels relative to the GaAs conduction 共valence兲 band obtained in this work. The proximity
of energy values determined with different procedures seems
to indicate that both the low-temperature flat signal and the
step originate from the same QD level, in contrast to the
two-level escape mechanism proposed in Ref. 7. Although
Coulomb charging effects prevent the observation of higher
excited states by space charge techniques,13 it is possible that
two or even more QD levels close in energy are responsible
for the C – V and DLTS spectra obtained here. In this case,

1

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