Magnetotransport in quantum cascade detectors: analyzing the current under illumination.

Abstract

Photocurrent measurements have been performed on a quantum cascade detector structure under strong magnetic field applied parallel to the growth axis. The photocurrent shows oscillations as a function of B. In order to describe that behavior, we have developed a rate equation model. The interpretation of the experimental data supports the idea that an elastic scattering contribution plays a central role in the behavior of those structures. We present a calculation of electron lifetime versus magnetic field which suggests that impurities scattering in the active region is the limiting factor. These experiments lead to a better understanding of these complex structures and give key parameters to optimize them further.

Full text

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NANO EXPRESSOpen Access
Magnetotransport in quantum cascade detectors:
analyzing the current under illumination
François-Régis Jasnot1, Nicolas Péré-Laperne1, Louis-Anne de Vaulchier1*, Yves Guldner1, Francesca Carosella1,
Robson Ferreira1, Amandine Buffaz2, Laetitia Doyennette2, Vincent Berger2, Mathieu Carras3, Xavier Marcadet3
Abstract
Photocurrent measurements have been performed on a quantum cascade detector structure under strong
magnetic field applied parallel to the growth axis. The photocurrent shows oscillations as a function of B. In order
to describe that behavior, we have developed a rate equation model. The interpretation of the experimental data
supports the idea that an elastic scattering contribution plays a central role in the behavior of those structures. We
present a calculation of electron lifetime versus magnetic field which suggests that impurities scattering in the
active region is the limiting factor. These experiments lead to a better understanding of these complex structures
and give key parameters to optimize them further.
Introduction
The quantum cascade detector (QCD) [1] recently pro-
posed and realized in both the mid-infrared [2] and the
THz [3,4] range is a photovoltaic version of the quan-
tum well infrared photodetector [5]. Their band struc-
ture are designed as quantum cascade lasers without
any applied bias voltage [1,3]. QCD are totally passive
systems and show a response only to photon excitation.
As such, the QCD structure is designed to generate an
electronic displacement under illumination through a
cascade of quantum levels without the need of an
applied bias voltage.
In a semiconductor quantum well structure, magnetic
field applied along the growth direction breaks the 2D
in-plane continuum into discrete Landau levels (LLs).
This experimental technique has been used to evaluate
the different contributions of scattering mechanism in
complex quantum cascade structures [5-9].
We present in this article experimental photocurrent
measurements under magnetic field applied along the
growth direction. We develop a simple model of trans-
port under illumination in a QCD. Through a compari-
son between experimental and calculation results, we
evidence the mechanism limiting the response of the
QCD.
Experimental setup and sample
The QCD under study is a GaAs/Al0.34Ga0.66As hetero-
structure with a detection wavelength of 8 μm as
described in ref. [9]. It consists of 40 identical periods of
7 coupled GaAs quantum wells. Figure 1 recalls the
principle of the device.
QCDs are mounted inside an insert at the center of a
superconducting coil where a magnetic field B up to
16 T can be applied parallel to the growth axis. Light is
emitted by a globar source from an FTIR spectrometer
and guided to the sample. The experiment consists in
measuring the current under illumination (Ilight) without
any applied voltage at 80 K while the magnetic field is
swept from 0 to 16 T.
Results
Experimental result is illustrated on Figure 2a. The
photocurrent shows oscillations as a function of the
magnetic field, superimposed on a continuous decreas-
ing background which is removed from the experi-
mental data in Figure 2b. Minima of current are
located at B = 10.1, 11.4, 13.0, and 15.3 T and are in
agreement with crossing of LL |up, 0〉 and LLs |down,
p〉 represented on Figure 2c. It leads to the conclusion
that an elastic scattering mechanism is dominant in
this structure and mainly involves the levels |up〉 and
|down〉.
* Correspondence: louis-anne.devaulchier@lpa.ens.fr
1Laboratoire Pierre Aigrain, Ecole Normale Supérieure CNRS (UMR 8551), 24
rue Lhomond, 75231 Paris Cedex 05, France.
Full list of author information is available at the end of the article
Jasnot et al. Nanoscale Research Letters 2011, 6:206
http://www.nanoscalereslett.com/content/6/1/206
© 2011 Jasnot et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution
License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium,
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Discussion
We propose a model of transport in one period based
on a rate equation approach. We assume that electrons
are in the upper detector state |up〉 through absorption
of a photon. Current as a function of lifetimes involved
in this structure can be written:
?
J
q= αNdown
τup-down
τup-down + τup-c
?
= αNdownQE.
(1)
The parameters a and Ndownare, respectively, the
absorption factor and sheet density of |down〉 and are
constant. The subscribe c stands for the whole cascade.
The quantum efficiency QE is the ratio of the lifetime
τup-downdivided by τup-down+ τup-cand corresponds to
the fraction of electrons on the level |up〉 that contri-
butes to the photocurrent. In our model we suppose
that any incident photon generates an absorption
between the levels |down〉 and |up〉.
We present in Table 1 the calculated scattering rates
of the different processes at B = 0 T. For interface
roughness, we used a Gaussian autocorrelation of the
roughness, with an average height of Δ= 2.8 Å and a
correlation length of Δ = 60 Å. LO phonon emission
scattering rate has been calculated as in ref. [10]. In our
structure impurities scattering is the most efficient pro-
cess [11]. Usually in GaAs quantum cascade structures
this mechanism is neglected because the doped layers
are not in the active region. In order to take into
account the main scattering process we calculate
ionized impurities scattering as a function of magnetic
field. The details of the calculation are presented else-
where [12].
Figure 3 represents a comparison between experimen-
tal data and electron-ionized impurities scattering time
as a function of magnetic field. Figure 3b, c shows the
two lifetimes involved in Equation 1 as a function of B
calculated with electron-ionized impurities scattering.
Figure 3d shows the calculation of the related quantum
efficiency.
The oscillating behavior at high magnetic field (B >
9T) is a result of the electronic transfer from |up〉 to |
down〉. This transfer leads to minima in the current
which fit well with τimp
up-downand QE. The long period
oscillating behavior of τimp
the peak at B = 14 T in QE in agreement with
up-cas a function of B enhances
Figure 1 Conduction band diagram of one period of an 8 μm
QCD showing the energy levels. Note that the ground state of
the first QW belongs to the former period and is noted |down〉. The
arrows illustrate the electronic path during a detection event. The
layer sequence is as follows 67.8/56.5/19.8/39.6/22.6/31.1/28.3/31.1
/33.9/31.1/39.6/31.1/45.2/50.8 (the barriers are represented in bold
types). The n-doping of the large QW is 5 × 1011cm-2.
Table 1 Calculated scattering rates in s-1
Scattering mechanism1/τup-down
7.0 × 1011
6.0 × 1011
1.8 × 1013
1/τup-c
7.2 × 1011
8.6 × 1012
5.2 × 1013
LO phonon emission
Interface roughness
Impurity scattering
Calculations are performed using different scattering processes for an electron
in the |up〉 subband at B = 0 T.
Figure 2 Experimental result and LL fanchart. (a) Current under
illumination as a function of B at 80 K and at zero bias. (b) Ilightas a
function of B where the decreasing background as been subtracted.
(c) Fan chart of |up, 0〉 and |down, p〉 as a function of B taking into
account the band non-parabolicity.
Jasnot et al. Nanoscale Research Letters 2011, 6:206
http://www.nanoscalereslett.com/content/6/1/206
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experimental data. QE, which describes the performance
of the detector, is oscillating between 74 and 85% under
B. By extrapolating, at B = 0T, QE is equal to 75%, a
value that should be increased to improve the detector
performance. An optimized structure should take these
results into account by shifting the ionized impurities
from the active region, where they are enhancing
τimp
up-down, to a position where they would only enhance
τimp
characteristic energy of 37 meV. This energy is attribu-
ted to transitions in the cascade involving an elastic
scattering mechanism.
up-c. The series of peak at B < 9T corresponds to a
Conclusion
In conclusion, we observe oscillations of the photocur-
rent in a mid-infrared QCD as a function of B. These
oscillations are due to electron-ionized impurities scat-
tering. This mechanism is dominant in this structure
because impurities are located in the active region. In
order to improve further this efficiency, we suggest to
shift the impurities in another location of the structure
in order to minimize τimp
The Laboratoire Pierre Aigrain is a “ Unité Mixte de
Recherche” between École Normale Supérieure, the
CNRS, the University Paris 6 and the University Paris 7.
up-down.
Abbreviations
LLs: Landau levels; QCD: quantum cascade detector.
Acknowledgements
This study has been supported by a grant of the Agence Nationale pour la
Recherche (ANR).
Author details
1Laboratoire Pierre Aigrain, Ecole Normale Supérieure CNRS (UMR 8551), 24
rue Lhomond, 75231 Paris Cedex 05, France.2Laboratoire Matériaux et
Phénomènes Quantiques, Université Denis Diderot - Paris 7, CNRS (UMR
7162), Bâtiment Condorcet, 75205 Paris Cedex 13, France.3Alcatel-Thales 3-5
lab, Route départementale 128, 91767 Palaiseau Cedex, France.
Authors’ contributions
FRJ, NPL and LAV performed magneto-transport experiment, analysed the
data and drafted the manuscript. YG, FC and RF participated in the analysis
of the data. AB, LD and VB designed the band diagram of the structure and
performed analysis. MC and XM have grown the sample by molecular beam
epitaxy. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Received: 16 July 2010 Accepted: 9 March 2011
Published: 9 March 2011
References
1.Gendron L, Carras M, Huynh A, Ortiz V, Koeniguer C, Berger V: Quantum
cascade photodetector. Appl Phys Lett 2004, 85:2824.
2.Gendron L, Koeniguer C, Berger V, Marcadet X: High resistance narrow
band quantum cascade photodetectors. Appl Phys Lett 2005, 86:121116.
3.Graf M, Scalari G, Hofstetter D, Faist J, Beere H, Linfield E, Ritchie D,
Davies G: Terahertz range quantum well infrared photodetector. Appl
Phys Lett 2004, 84:475.
4.Scalari G, Graf M, Hofstetter D, Faist J, Beere H, Linfield E, Ritchie D: A THz
quantum cascade detector in a strong perpendicular magnetic field.
Semicond Sci Technol 2006, 21:1743.
5. Levine BF, Choi KK, Bethea CG, Walker J, Malik RJ: New 10 μm Infrared
detector using intersubband absorption in resonant tunneling GaAlAs
superlattices. Appl Phys Lett 1987, 50:1092.
6.Smirnov D, Drachenko O, Leotin J, Page H, Becker C, Sirtori C, Apalkov V,
Chakraborty T: Intersubband magnetophonon resonances in quantum
cascade structures. Phys Rev B 2002, 66:125317.
7.Leuliet A, Vasanelli A, Wade A, Fedorov G, Smirnov D, Bastard G, Sirtori C:
Electron scattering spectroscopy by a high magnetic field in quantum
cascade lasers. Phys Rev B 2006, 73:085311.
8.Péré-Laperne N, de Vaulchier L-A, Guldner Y, Bastard G, Sacalari G,
Giovannini M, Faist J, Vasanelli A, Dhillon S, Sirtori C: Inter-Landau level
scattering and LO-phonon emission in terahertz quantum cascade laser.
Appl Phys Lett 2007, 91:062102.
9.A Péré-Laperne N, de Vaulchier L-A, Koeniguer C, Vasanelli A, Nedelcu A,
Marcadet X, Guldner Y, Berger V: Dark current analysis of quantum
cascade detectors by ma- gnetoresistance measurements. Phys Rev B
2008, 77:085307.
10.Becker C, Vasanelli A, Sirtori C, Bastard G: Electronlongitudinal optical
phonon interaction between Landau levels in semiconductor
heterostructures. Phys Rev B 2004, 69:115328.
Figure 3 Comparison between experimental data and electron-
ionized impurities scattering time as a function of B. (a) Ilightas
a function of the magnetic field where the background has been
subtracted. (b) Ionized impurity scattering τimp
magnetic field between |up〉 and |down〉 levels. (c) Ionized impurity
scattering τimp
up-cunder magnetic field between |up〉 and levels in
the cascade. (d) QE calculated with Equation (1).
up-downunder
Jasnot et al. Nanoscale Research Letters 2011, 6:206
http://www.nanoscalereslett.com/content/6/1/206
Page 3 of 4

Page 4

11.Ferreira R, Bastard G: Evaluation of some scattering times for electrons in
unbiased and biased single- and multiple- quantum-well structures. Phys
Rev B 1989, 40:1074.
Jasnot F-R, Péré-Laperne N, de Vaulchier L-A, Guldner Y, Carosella F,
Ferreira R, Buffaz A, Doyennette L, Berger V, Carras M, Berger V:
Photocurrent analysis of quantum cascade de- tectors by
magnetotransport. Phys Rev B 2010, 82:125447.
12.
doi:10.1186/1556-276X-6-206
Cite this article as: Jasnot et al.: Magnetotransport in quantum cascade
detectors: analyzing the current under illumination. Nanoscale Research
Letters 2011 6:206.
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