Table Of ContentExcited two-dimensional magnetopolaron states in quantum well
of resonant tunnel junction
D.Yu. Ivanov1, M.V. Chukalina1, E.G. Takhtamirov2, Yu.V. Dubrovskii1, L. Eaves3,
V.A. Volkov2, E.E. Vdovin1, J.-C. Portal4,6,7, D.K. Maude4, M. Henini3, G. Hill5.∗
1 Institute of Microelectronics Technology RAS,
5
142432 Chernogolovka, Russia
0
0 2 Institute of Radioengineering and Electronics RAS, Moscow, Russia
2 3 The School of Physics and Astronomy,
University of Nottingham, Nottingham NG7 2RD, UK
n 4 Grenoble High Magnetic Field Laboratory,
a
MPI-CNRS, BP166 38042 Grenoble Cedex 9, France
J
5 Department of Electronic Engineering,
3
University of Sheffield, Sheffield S1 3JD, UK
1 6 Institut Universitaire de France, 103,
Boulevard Saint-Michel, 75005 Paris, France
l] 7 INSA, F31077 Toulouse Cedex 4, France
l
a (Dated: February 2, 2008)
h
Tunnel spectroscopy is used to probe the electronic structure in GaAs quantum well of resonant
-
s tunneljunction over wide range of energies and magnetic fieldsnormal tolayers. Spin degenerated
e highLandaulevels(N =2÷7)arefoundtobedrasticallyrenormalisednearenergieswhenthelon-
m gitudinaloptical-phonon(~ωLO)andcyclotronenergy(~ωC)aresatisfiedcondition~ωLO =m~ωC,
. wherem=1,2,3. Thisrenormalisationisattributedtoformationofresonantmagnetopolarons,i.e.
t
a mixing of high index Landau levels by strong interaction of electrons at Landau level states with
m LO-phonons.
-
d
n In polar semiconductors, such as GaAs, electrons in- theQWbymeansofbothelasticandinelastictunnelling
o teract with LO phonons to form polarons, i.e. the bare spectroscopy. The phonon assisted tunnelling channel is
c electron states are renormalized. If a magnetic field B opened independently of sample quality. As the result
[
is applied perpendicular to the plane of the GaAs quan- we have found strong interaction between LL’s of differ-
1 tum well, 2D electron states are quantized into Landau ent indices (N = 2÷7) in the well near energies when
v levels (LL) of index N. Filling of empty Landau lev- thelongitudinaloptical-phonon(~ω )andcyclotronen-
LO
9 els in the QW by tunnelling current causes excitation ergy (~ω ) are satisfied condition ~ω =m~ω , where
C LO C
1 of resonantmagnetopolarons1,2 when resonantcondition m = 1,2,3. This was attributed to formation of reso-
3 n~ω = m~ω , where n,m are integers, is satisfied. nant magnetopolaronstates, i.e. mixing of different LLs
1 LO C
The resulting magnetopolarons can be measured experi- by interaction with LO-phonons.
0
5 mentally by monitoringdensity ofstates in the quantum Samples grown by MBE comprised (in the order of
0 well by tunnel spectroscopy. Previously only interaction
growth): a lightly Si-doped, 300-nm–thick GaAs layer
at/ oonfegsrovuinadLLOa-npdhaounosntastheaNve=be0enwidtheteNcte=d1byanmdeNans=o2f ((NNd ==23·1·0110718cmc−m3−);3)a; 5a0.45-0n.4m-n–tmh–ictkhicukndGopaeAdsGlaayAesr
m phonon assisted tunnelling spectroscopy3. It was dis- d
spacer layer; a 8.3-nm–thick Al Ga As barrier layer;
0.4 0.6
- playedasanticrossingofthepositionofthepeaksrelated
a 5.6 nm undoped GaAs layer; a 1.8 monolayer (ML)
d
tothedoublephononassistedtunnellingintoLL(N =0)
n InAs (with growth rate 0.13 ML/s to form InAs QD);
andsingle phononassistedtunnelling into LL (N =1,2)
o a 5.6-nm–thick undoped GaAs layer; a 8.3-nm–thick
in the fan diagram.
c Al Ga As barrier; a 50.4 nm undoped GaAs; a 50.4-
0.4 0.6
v: In this work we present studies of electron struc- nm–thick GaAs layer (Nd = 2·1017 cm−3); and a 300-
i nm–thick GaAs layer (N = 3 · 1018) cap-layer. The
X ture of the QW in a magnetic field normal to the d
samples were characterised by photoluminescence (PL)
well plane by means of tunnel spectroscopy. The Al-
r spectroscopy, which confirmed the existence of the cor-
a GaAs/GaAs/AlGaAsheterostructurewasdoublebarrier
responding QD or WL emission. Ohmic contacts were
structure incorporating a layer of InAs quantum dots
obtained by successive deposition of AuGe/Ni/Au lay-
(QD) in the center of the well. The dots are charged
ers and subsequent annealing. Mesa structures, with di-
and create a considerable amount of disorder in the
ameter between 20 µm and 400 µm, were fabricated by
well. In this case the number of elastic scattering as-
conventionalchemical etching.
sisted tunnelling events with only energy conservation,
but not momentum conservation is increased consider- The band diagram of the structure under voltage bias
ably. It means that direct tunnelling between different is shown in Figure 1(a). With the application of a suf-
LL’s in the emitter and collector is permitted and one ficient bias to the structure, an accumulation layer is
can monitor the density of states in a magnetic field in formed adjacent to the barrier, which serves as two-
2
FIG. 1: (a) The band diagram of the structure under voltage bias; (b) variation of tunnelling current versus magnetic field
at Vbias = 230 mV; (c) variation of tunnelling current versus reverse magnetic field at Vbias = 230 mV; (d) result of Fourier
transform; (e) result of WL transform.
dimensional emitter. The details of resonant tunnelling 28
LL1+hω
through this double barrier structures with disorder in- 26 LO
troduced by QD was published earlier4. The tunnelling 24
current oscillates with varying magnetic field with con- T 22 LL2+hω
stantbias appliedto structure(Fig.1(b)). Peaksareob- ond, 20 LO
served,correspondingtotunnellingintoLandaustatesof ositifiel 18 LL3 LL4
thegroundsubbandinthewellwithandwithoutphonon akpnetic 1146 LL3+hωLO
wemhiesnsioonnl.yWtheealnowaleyssteeonnelrygythLeadnadtaaufloervefileilsdsocacbuopvieed4Tin, entpesmag 1102 LL4 LLLL54++hhωωLO
the emitter. All measurements were carried out at tem- urrsu 8 LO
perature T =4K. Cver 6
CarefulanalysisoftheexperimentaldataateachVbias 4
allowed us to identify all peaks in a magnetotunnelling 2 LL7
spectrum. Three different techniques have been used to 0
do this: identification of peak position in 1/B vs. LL 0 50 100 150 200 250 300 350 400
number,Fourieranalysis,andmoresophisticatedwavelet Current peakposition
analysis. The wavelet analysis4 is a mathematical tool, versusbias,mV
whichallowstodecomposeasignalinthelocallyconfined
FIG.2: Fandiagramsummarisedpeakpositionsversusmag-
waves (Wavelets).
netic field in tunnelling spectra. Solid circles - position of
The general expression for WL transform is
peaksduetophononassistedtunnelling. Opencircles-direct
(Tf)(a,b) = |a|−12 R dtf(t)ψ(t−b) , where ψ(t) is so tunnellingfromthegroundLandaulevelN =0intheemitter
a
called ”mother” wavelet function. The transform result toLandaulevelofhigherindexesinthequantumwell. Inthe
is a function of two variables. Parameter (1) is analog fandiagram itiseasytoseeregionswheredifferentlevelsare
a
of frequency in the Fourier transform. Each ψ(t−b) is anticrossing. These regions are indicated by circles.
a
localized around t = b . For WL decomposition of our
experimental data we have used the Morlet5 ”mother”
function ψ(t) =(exp(iγt)−exp(−γ2))exp(−t2) , which showsresultof WL transform. This is the 3-dimensional
is a trigonometricfunction modulat2ed by Gau2ssian. The picture, where the amplitude AWL = Re[(Tf)(a1,b)] of
parameter γ determines the number of oscillations one the Wavelet transform (z-axis) is presented versus fre-
wants to use for the analysis and should be optimised quency (y-axis) and the inverse magnetic field (x-axis).
in each specific case. In more details the procedure of As usual tunnelling with and without phonon emission7
wavelet analysis is described in paper6. results in two sets of oscillations periodical in reverse
The result of WL analysis of tunnelling spectra magnetic field in tunnelling spectrum at constant bias,
recorded at 230 mV is shown in Figure 1. Fig. 1(b) with frequencies BFLO = me~∗(EEm −EQW −~ωLO) and
and Fig. 1(c) show recorded signal versus magnetic field BEl = m∗(E −E ) respectively. Here m∗ and e
F e~ Em QW
and reverse magnetic field respectively. The result of are the effective mass and charge of an electron; ~ is
Fourier transform is shown in Fig 1(d). Figure 1(e) the Plank constant; E , E , are the energies of the
Em QW
3
FIG.3: ThisfigureillustratesstronginteractionbetweenN=2andN=4LandaulevelsinmagneticfieldaroundB=10Twhen
2~ωC =~ωLO,detailsareinthetext. (a)WavelettransformofthetunnellingspectraatVbias =162mV;(c)atVbias=175mV;
(e) atVbias =187 mV;(b)variation oftunnellingcurrentversusreverse magnetic fieldfor Vbias=162 mV;(d)forVbias =175
mV; (f) for Vbias=187 mV;(g) schematic presentation of theidentified magnetopolaron states.
groundquasiboundstatesintheemitterandinthequan- of the smaller amplitude with direct tunnelling into LL
tumwell(QW)respectively,~ω isthelongitudinalop- withN =4). Inthiswaywehaveidentifiedallthepeaks
LO
tical phonon energy. Peaks in the tunnelling spectrum in the tunnelling spectra at different bias voltages. Fan
related to phonon assisted tunnelling into LL belong to diagram in Figure 2 summarised peak positions versus
low frequency set of oscillationand the elastic scattering magnetic field in tunnelling spectra. Solid circles - posi-
peaksto highfrequency set. Fouriertransformspectrum tion of peaks due to phonon assisted tunnelling. Open
(Fig. 1(d)) shows evidently two frequencies separatedby circles - direct tunnelling from the ground Landau level
∆B = 21.4 T. Than ∆B e~ = 37 meV, which is equal N = 0 in the emitter to Landau level of higher indexes
m∗
to energy of LO-phonon (36 meV) in GaAs with good in the quantum well.
accuracy as expected. Wavelet transform permits one
to determine the origin of each peak in the tunnelling StronginteractionbetweenLLofdifferentindexeshave
spectrum. For example, arrows labelled by ”E” in Fig- been observed in tunnelling spectra ~ωLO =m~ωC with
ures 1(b) and 1(c) indicate the same peak. Appropriate m=1,2,3. ThedetailsofthisinteractionbetweenN =2
maximum in the amplitude A of the Wavelet trans- and N = 4 Landau levels (m = 2) is shown in Figure 3,
WL
form(Figure1(e)),alsoindicatedbyarrow”E”. Wavelet as example. Tunnelling spectra versus reverse magnetic
dataindicatethatthepeakbelongstothehighfrequency field for three different biases are presented in Figures
set of oscillations and therefore is related to the elastic 3(b), (d), and (f). Figures 3(a), (c), (e) show Wavelet
tunnelling into LL with N = 3. The LL index could transforms of the tunnelling spectra, respectively. Since
be easy determined by standard procedure. In the same these peaks move versus bias with different velocity, one
manner one can conclude that peak labelled by ”P” ap- couldexpectthatwithoutinteractiontheyshouldcrossed
pearsduetothephononassistedtunnellingintoLLwith at the intermediate bias voltage, Vbias =175 mV in this
N =2. (More precisely one should say that peak ”P” is case. Contrary we see typical anticrossing behaviour of
the superposition of two peaks, one with higher ampli- the peaks, first, the exchange of oscillator intensity, sec-
tuderelatedwithphononassistedtunnellingandanother ond, the same peak is relatedto directtunnelling on one
side or phonon assisted-tunnelling on another side away
4
from strong interaction point. Circles in the fan dia- optical phonons, for electron tunnelling into a quantum
gram (Figure 2) indicate the regions where different lev- well with embedded quantum dots.
els are anticrossing. Next magnetopolaron states have
been identified in this work:
~ω =~ω =E −E Acknowledgments
LO C LL3 LL2
~ω =2~ω =E −E =E −E
LO C LL5 LL3 LL4 LL2
~ω =3~ω =E −E =E −E This work was supported by RFBR (04-02-16870,
LO C LL7 LL4 LL6 LL3
02-02-22004), PICS (1577), RAS programs ”Quantum
This is illustrated in Figure 3(g). Macrophysics”,and”Low-DimensionalQuantumNanos-
In conclusion, we have observedandidentified a set of tructures”, FTNS program, EPSRC, and RS (UK). We
two-dimensionalresonantexcitedmagnetopolaronstates, are grateful to Dr. H. Funke for the support during the
i.e. mixing of different high indexes Landau levels by software development.
∗ Electronic address: [email protected] 5 A. Louis, P. Maass, and A. Rieder, Wavelets: Theory and
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