Electron cyclotron mass in undoped CdTe/CdMnTe quantum wells

0.16 MB·

by  A. A. Dremin

Electron cyclotron mass in undoped CdTe/CdMnTe quantum wells
A.A. Dremin1,2, D.R. Yakovlev1,3, A.A. Sirenko4, S.I. Gubarev2, O.P. Shabelsky2, A. Waag5, and M. Bayer1
1Experimentelle Physik II, University of Dortmund, D-44227 Dortmund, Germany
2Institute of Solid State Physics, Chernogolovka, Moscow district, 142432, Russia
3A.F.Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
5 4New Jersey Institute of Technology, Newark, NJ 07102, USA
0 5Institute of Semiconductor Technology, Braunschweig Technical University, 38106 Braunschweig, Germany
0 (Dated: February 2, 2008)
2
Opticallydetectedcyclotronresonanceoftwo-dimensionalelectronshasbeenstudiedinnominally
n
undopedCdTe/(Cd,Mn)Tequantumwells. Theenhancementofcarrierquantumconfinementresults
a
J in an increase of the electron cyclotron mass from 0.099m0 to 0.112m0 with well width decreasing
from 30 down to3.6 nm. Model calculations oftheelectron effectivemass havebeen performed for
1
thismaterialsystemandgoodagreementwithexperimentaldataisachievedforanelectron-phonon
2 coupling constant α=0.32.

]
l PACSnumbers: 76.40.+b,73.21.Fg,71.35.Pq,78.55.Et
l
a
h
- I. INTRODUCTION under absorption of microwave or FIR radiation by free
s
carriers. Itwas provedto be extremely sensitiveand has
e
m The effective masses of carriers (electrons and holes) been successfully usedto measurethe effective massesof
electronsandholesinbulkGaAs,InP,CdTe[5,6,7],and
. are among the basic parameters for semiconductors and
t SiC[8]. Itwasalsodevelopedtostudy2Delectronstates
a semiconductor heterostructures. Nowadays exhaustive
m informationisavailableforheterostructuresbasedonIII- inGaAs/(Al,Ga)Asheterostructures[9,10,11]andinter-
nal transitions of neutral and charged magnetoexcitons
- V semiconductors, e.g. GaAs/(Al,Ga)As heterosystems.
d However, only limited experimental data have been re- [12, 13, 14]. Another advantageof the ODR technique is
n related to its spectral selectivity, which allows for select-
ported so far for the II-VI family of semiconductor het-
o ing the signal from different quantum wells grownin the
erostructures. Among them are the structures based on
c same structure by analyzing the corresponding photolu-
[ CdTe, which are rather popular for optical studies. One
ofthe attractionsto this materialis the possibility toin- minescenceemissionlines. Therefore,theODRtechnique
1 is very well suited for measurements of the electron ef-
troduce magnetic Mn-ions in the cation sublattice. The
v fective masses in undoped CdTe-based QWs of different
strongexchangeinteractionoffreecarrierswithlocalized
6 widths.
1 spinsofmagneticionsgivesrisetogiantmagneto-optical
5 effects,e.g. thegiantZeemansplittingofthebandstates,
1 giant Faraday rotation, etc. [1]. (Cd,Mn)Te, (Cd,Mg)Te
0 and(Cd,Zn)Teareamongthebarriermaterialstoconfine II. EXPERIMENT
5
carriers in CdTe quantum wells. In this paper we study
0
/ experimentally the dependence of the electron effective We have studied a CdTe/Cd0.86Mn0.14Te quantum
at massonquantumwell(QW)widthforCdTe/(Cd,Mn)Te heterostructure grown by molecular beam epitaxy on
m heterostructures. an (100)-oriented CdTe substrate. The structure con-
The cyclotron resonance (CR) technique is widely tains four consequently grown CdTe wells with width
-
d used for evaluation of the fundamental parameters of L =30, 9, 3.6 and 1.2 nm separated by 50-nm-thick
Z
n heterostructures, including the carriers effective masses. Cd0.86Mn0.14Tebarriersfromeachother. Typicalphoto-
o It has been recently applied to modulation-doped luminescence (PL) and reflectivity spectra of such struc-
c
CdTe/(Cd,Mg)Te QWs and the electron effective mass tures can be found in [15, 16, 17].
:
v hasbeenmeasuredfortheseQWswithwidthsvariedbe- Experiments were carried out at a temperature of
Xi tween 7.5 and 30 nm [2, 3] each, with a 2D electron gas T = 4.2 K in a He exchange cryostat in magnetic fields
density of 4×1011 cm−2. One of the impediments for up to B = 8.3 T. The sample was mounted on a rotat-
r
a the conventional cyclotron resonance technique is that ingplatform,whichenablesODRmeasurementsintilted
the carrier density has to be large enough to produce a magnetic fields in order to check the two-dimensional
noticeable change in the absorption of microwave or far- character of the studied resonances. Most experimental
infrared (FIR) radiation. This limitation does not allow datawerecollectedinmagneticfieldsorientedparallelto
to measure carrier effective masses in undoped systems. thestructuregrowthaxis(θ =0◦)withthecyclotronmo-
It has been overcome by invention of the Optically De- tionofelectronsinthe planeofthe quantumwells. Pho-
tected of Cyclotron Resonance (ODCR, or ODR) tech- toexcitationofthesamplesbyaHeNelaserandcollection
nique (see [4] and references therein). oftheluminescencesignalwasprovidedviaopticalfibers.
The ODR technique is based on variation of the op- The spotofthe HeNe laserbeam(λ=6328˚A,powerup
tical properties, such as the photoluminescence intensity to20mW)wasoverlappedbythespotofaCO2 pumped
2

30 nm QW a) 9 nm QW b) 3.6 nm QW c)
4
B = 6.47 T B = 6.8 T B = 7.35 T
T
3 X X
a.u.) X T
sity ( 2 T
n
e
nt
L i 1
P
0
R
D -1
O
x20 x100 x100
-2
1.590 1.595 1.600 1.610 1.615 1.620 1.66 1.67 1.68 1.69
Energy (eV)
FIG.1: PhotoluminescenceandODRsignalspectrameasuredforCdTe/Cd0.86Mn0.14TeQWswithwidthsequalto: (a)30nm,
(b) 9 nm, and (c) 3.6 nm. Spectra are measured at magnetic fields for which the FIR radiation induces themaximal changes,
i.e. under conditions of cyclotron resonance for electrons. T=4.2K. The photon energies corresponding to the maximum of
theODRsignal are marked with arrows. Notethat themagnetic fieldsscans of thecyclotron resonances shown in Fig. 3were
detected at these energies.
FIRlaser. Farinfrared(FIR)radiation(λ =163µm, which is about an order of magnitude smaller than the
FIR
E =7.6 meV) with a power up to 15 mW was guided binding energy of the quasi-2D excitons.
FIR
into the cryostat via a stainless steel pipe and focused One can also see in Fig. 1 that the exciton emission
onthe sampleby a Teflonlens. Photoluminescence(PL) line shifts from 1.597 up to 1.678 eV for QW width var-
signal was analyzed with a 0.6 m grating spectrometer ied from 30 down to 3.6 nm due to the carrier quantum
equipped with a cooled photomultiplier. confinement. We use the energy position of the exciton
The FIR laser beam was mechanically chopped. The emission to evaluate the QW width for the studied sam-
influenceoftheFIRradiationonthePLspectrawassyn- ples. ModelcalculationsfortheexcitonPLtransitionen-
chronouslydetectedbyalock-inamplifieratvariousmag- ergyandtheexcitonbindingenergyhavebeenperformed
netic fields. The ODR signal was normalized to the PL using the procedure described in [19] with the following
intensity I(B) measured at the same wavelength. This parameters for our material system: the band gap offset
procedure allowed us to correct the shape of the reso- between the well and barrier materials is 223 meV, it is
nance profile by accounting for the PL intensity varia- divided in a ratio of 70/30 between the conduction and
tions with increasing magnetic field. valence bands; the dielectric constantε=10;the in-plane
heavy-holemasswastakenasmhh,k=0.37m0;the heavy-
hole mass along the growth axis, i.e. perpendicular to
III. RESULTS AND DISCUSSION theQWplane,ismhh,⊥=0.48m0. Wehavetakenintoac-
counteightconfinedelectronlevelsandtenconfinedhole
Photoluminescence spectra for three levels. The results of our calculations are presented in
CdTe/Cd0.86Mn0.14Te QWs are shown in Fig. 1. Fig. 2, from which the widths of the quantum wells have
The emission spectra of all three QWs consist of two beendeducedbycomparingtheexperimentalexcitonPL
strong lines corresponding to excitons (X) localized transition energies with the calculated dependence.
at well-width fluctuations and to charged exciton We turn now from the sample characterization to the
complexes, i.e. trions (T) consisting of two electrons results of the optically detected resonance. ODR sig-
and one hole [18]. Their formation requires excess of nal could be reliably detected in the QWs with widths
electrons over holes in QWs. Such excess is typical LZ =30, 9 and 3.6 nm. We have found no influence
for unintentionally doped CdTe QWs, due to carrier of FIR on the emission from the narrowest QW with
diffusion from the barrier materials with residual n-type LZ =1.2 nm. Most probably the changes are below the
doping. The energy difference between the exciton and sensitivity level of our setup.
trion lines varies from 2.5 to 5 meV and increases in The ODR signal intensity plotted as a function of
narrowwells. Itcorrespondsto the trionbinding energy, magnetic field clearly demonstrates a resonance behav-
3

which is directly linked to the value of the electron ef-
25 CdTe/Cd Mn Te QWs
0.86 0.14 fective mass; (ii) the resonance full width at the half
eV) 1.75 V) maximum (FWHM), which is inversely proportional to
y (m 20 binding energy y (e the electron scattering rate and contains information on
nerg 15 1.70 nerg twhheicehleicstcroonntmroollbeidlitbyy,tahnedm(ieici)hatnhiesmressorensapnocnesaibmlepfloitrutdhee,
e e
g e1-hh1 n ODR signal. Before proceeding with discussion of the
n o
ndi 10 1.65 siti resonance parameters we shall proof that the observed
on bi 5 Tran ftewaot-udriemseonrsiigoinnaaltechfaroramcttehreofQeWlecst.roInnsorredsperontsoibclheefcokrtthhee
cit exciton ODR signal we have carriedout the same measurements
x 1.60
E
intiltedmagneticfields. ThepronouncedshiftoftheCR
0
0 5 10 15 20 25 30 resonancetowardhigher magnetic fields was found to be
proportional to 1 / cosθ where θ (being varied from 0˚
QW width (nm)
to 24˚)is the anglebetweenthe magnetic fielddirection
and the structure growth axis. The insert in Fig. 3 illus-
FIG.2: Excitonenergy,excitonbindingenergyandenergyof
trates this observation for the 30 nm QW proving that
optical transition between the lowest levels of confined elec-
tronsandholes(e1-hh1)calculatedforCdTe/Cd0.86Mn0.14Te the electrons have quantum confined character.
QWs as function of theQW width. In the widest QW with 30 nm width, the resonance
FWHM is 0.33 T. This corresponds to a momentum re-
laxation time of 2.4 ps, and to an electron mobility of
E = 7.6 meV
0 FIR 3.0×104 cm2/(V·s). A decrease of the well width is ac-
companied by a strong broadening of the resonances up
to 0.74 T and 1.9 T for 9 nm and 3.6 nm wells, respec-
u.) -1 tively. Thecorrespondingelectronmobilitiesare1.4×104
a. and0.5×104cm2/(V·s). LocalizationofelectronsonQW
(
al -2 widthfluctuationsisknowntobethedominatingmecha-
n 3.6 nm nism for resonance broadening in low dimensional struc-
g
si BR (T) tures. Its contribution increases in narrow QWs causing
R -3
7.0 the decrease of the carrier mobility. It goes in line with
D
O 6.8 9 nm the increasing width of the photoluminescence emission
-4 6.6 spectra from 1.7 meV to 3.7 meV for 30 nm and 3.6 nm
wells, respectively (see Fig. 1).
6.4
-5 1.00 1 /1 C.0O4SQ(1QQQ.0)8 30 nm T = 4.2K The modulation spectra (ODR signal) recordedat the
resonance magnetic field are shown in the lower panels
of Fig. 1. In the 30 nm QW the FIR radiation results
5 6 7 8
Magnetic field (T) in a decrease of the PL signal by approximately 2.5%
for the trion line and a significantly smaller decrease for
FIG.3: MagneticfielddependenceofODRsignal atEFIR = the exciton line. The ODR signal decreases in narrower
7.6 meV measured in CdTe/Cd0.86Mn0.14Te QWs. The shift QWs,itisabout0.9%forthe9nmQWandonly0.5%for
the 3.6 nm QW. This observation can be attributed to
of the resonance field is given in the insert as function of
thetilt angleθ for the30-nm-wideQW (circles –experiment enhanced electron localization and the related decrease
values; line – fit with 6.45/cos(θ)). of the electron mobility in narrow QWs.
The dominating mechanism of the PL intensity mod-
ulation under FIR radiation is related to the specifics of
ior (Fig. 3). We have checked that both the resonance thetrioncomplexesinthestudiedstructures. Asonecan
field and the shape of the resonance profile are insensi- seeinFig.1,thestrongestODRsignalhasbeenobserved
tive to the PL detection energy. The ODR signal was inthemaximumofthetrionemissionlineandonlyweak
recordedatfixeddetectionenergiesshownby the arrows modulations are seen for the exciton line. This is ex-
in Fig. 1. The ODR signal was normalized to the PL pectedsince inQWswith averydilutedelectrongasthe
intensity measuredat the same detection energy. For all trionemissionismuchmoresensitivetothe temperature
QWsthePLintensitywasdecreasingbyabout30%with of the electron gas [18, 20] then the exciton emission.
increasing magnetic field from 5.5 T to 8 T. This change This is due to the fact that for the trion formation one
has very small influence on the shape of the resonance of the electrons is captured from the electron gas and,
profile and requires correction of the resonance field by hence, the probability of the trion formation is very sen-
less than 0.01 T. sitive to the electron gas temperature. Heating of the
Therearethree characteristicsofthe resonancecurves electronsunder cyclotronresonanceconditions decreases
to be analyzed: (i) the resonance magnetic field B , the probability for trion formation, which causes a de-
R
4

crease of the trion emission intensity. 0.115
CdTe/(Cd,Mn)Te QWs
Measurement of the resonance magnetic field BR, m0 CdTe/(Cd,Mg)Te QWs
werhgeyreoftheleecFtrIoRnse,naelrlgoywscoeivnacliudaetsiownitohf tthheeeclyecctlorotrnoneffeenc-- m / e0.110
tive mass. Fitting the resonances shown in Fig. 3 by s 2D polaron mass
s
a Lorenzian function we obtained BR = 6.45, 6.75 and a 0.105
m
7.25 T for QWs with L = 30, 9 and 3.6 nm, respec-
Z e
tively. The electron cyclotron mass m was evaluated v
from BR values using me/m0 =0.0152 BeR [T], which is ecti 0.100
derived from me = e~BR/EFIR for EFIR= 7.6 meV. eff bulk CdTe
We found that me increases with decreasing well width: on 0.095 k*p
me = 0.099m0, 0.104m0 and 0.112m0 for LZ = 30, 9 ctr
and 3.6 nm. These data are shown by solid circles in e LMTO
El
Fig. 4. The arrow in the figure marks the electron effec- 0.090
tive mass of 0.096m0 measured for bulk CdTe [21]. The
open circles are experimental data for CdTe/(Cd,Mg)Te 0 5 10 15 20 25 30
QW width (nm)
QWs with non-magnetic barriers taken from [2]. These
resultscoincidewellwithourexperimentaldata. Forthe
FIG. 4: Electron cyclotron mass versus QW width for
studied relatively wide QWs the dominating part of the
CdTe-based quantum wells. Experimental data of this
electronwave function is concentratedin the CdTe wells
work for CdTe/Cd0.86Mn0.14Te QWs are given by closed
and is not much dependent on the differences in barrier
circles. Open circles show the data for the modulation-
materials. Also, the (Cd,Mn)Te and (Cd,Mg)Te alloys
doped CdTe/Cd0.88Mg0.12Te QWs with electron density of
areprettysimilarintheirpropertiesasthese barrierma- 4×1011 cm−2 [2]. The bare electron mass calculated without
terialsprovideefficientconfinementofbothelectronsand polaron correction inparabolic-band approximationisshown
holes. One may expect that in doped CdTe/(Cd,Mg)Te by the dashed line and that with accounting for conduction
QWsm willbelargerduetonon-parabolicityofthecon- band non-parabolicity is given by the dotted line. The solid
e
duction band at finite k-values given by the Fermi level. lineshowsthecalculationafterincludingtheelectron-phonon
However,anestimationofthiseffectfortheelectronden- interaction with α=0.32.
sity of 4×1011 cm−2 gives an m increase by 1.2% only
e
[2], which does not exceed the error bar for our exper-
imental data. Comparing the data for the two systems whereE =21.0eVistheinterbandmatrixelement,∆
P so
with differentbarriermaterialswe canconcludethat the = 0.93eV is the spin-orbitsplitting, E = 1.59eV is the
g
electron confinement and the respective increase of the fundamental band gap of CdTe, and F = -0.6 is a pa-
quantum confinement energy is the dominating factor in rameteraccountingforcontributionofhighenergybands
the me dependence on the QW width. [22, 23, 24]. One can see from Eq.(2) that the effective
For deeper insight into the electron mass behaviour mass m increases for largerband gapvalues. Exactcal-
b
we have compared the experimental data with results of culation of m in QW structures requires laborious nu-
b
model calculations. We will follow the commonly used merical procedures, which include the quantum confine-
routine in which the bare effective mass mb is calculated mentenergy,conductionbandnon-parabolicity,andpen-
and the polaron correction to the effective mass is fitted etration of the electron wave function into barriers (see
with the coupling constant of the electron-phonon inter- e.g. [25]). However,the3-bandk·papproachgivesfairly
action α used as a free parameter well suited values when E in Eq.(2) is replaced by the
g
energy separation between the lowest electron and hole
subbands. In Fig. 4 these calculations for CdTe-based
m =m (1+πα/8). (1) QWs in parabolic band approximationare shown by the
e b
dashedline. Inordertotakeintoaccounttheconduction
Thepolaroncontributiontothemeasuredcarriereffec- bandnon-parabolicityinCdTe,weperformedmoreelab-
tive masses originates from the cloud of optical phonons orate calculations based on density functional theory in
that “accompany” the electron and make the measured local density approximation using the linear muffin-tin-
mass “heavier”. For example, in bulk CdTe the calcu- orbital (LMTO) approach [26]. Calculated dependence
lated bare electron effective mass is 0.088m0 and the for the bare electron mass (the dotted line in Fig. 4)
measured polaron mass is 0.096m0. demonstrates the main experimental trend of increasing
mass values with narrowing QW width.
A simple analytical approach to calculation of m is
b
provided in the frame of 3-band k·p technique Verygoodagreementwithexperimentaldatahasbeen
achieved by correcting the bare mass with the polaron
effect using Eq.(1). The best fit shown by the solid
m0 EP (Eg +2∆SO/3) line has been achieved for α = 0.32. This value is in
=(1+2F)+ , (2)
m E (E +∆ ) goodagreementwiththeliteraturedatafortheelectron-
b g g SO
5
phonon interaction constant reported for CdTe and achievedwith an electron-phononinteractionconstantα
CdTe/(Cd,Mn)Te QWs (see [27]andreferencestherein). equal to 0.32.
To conclude, the optically-detected resonance tech-
nique has been used to study electron cyclotron res-
onance in nominally undoped CdTe/(Cd,Mn)Te QWs.
Acknowledgments
Pronouncedmodulationoftheluminescenceintensityhas
been found for the charged exciton emission, when the
residualelectronsareresonantlyheatedbyFIRradiation. This work was supported by the QuIST program of
Theevaluatedelectroneffectivemassesincreasewithnar- DARPA, the ’Forschugsband Mikro- und Nanostruk-
rowing quantum well width and are in good agreement turen’oftheUniversityofDortmund,the BmBFproject
withdataforCdTeQWsconfinedby(Cd,Mg)Tebarriers. ’nanoquit’ and the Russian Foundation for Basic Re-
Good quantitative agreement with model calculations is search.
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