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DETERMINATION OF BANDOFFSETS AND EXCITON BINDING IN CdTe/(Cd,Mn)Te
QUANTUM WELLS
S.-K. Chang, A. Nurmikko, Ji-Wei Wu, L. Kolodziejski, R. Gunshor
To cite this version:
S.-K. Chang, A. Nurmikko, Ji-Wei Wu, L. Kolodziejski, R. Gunshor. DETERMINATION OF
BANDOFFSETS AND EXCITON BINDING IN CdTe/(Cd,Mn)Te QUANTUM WELLS. Journal
de Physique Colloques, 1987, 48 (C5), pp.C5-367-C5-371. �10.1051/jphyscol:1987579�. �jpa-00226783�
DETERMINATION OF BANDOFFSETS AND EXCITON BINDING IN CdTe/(Cd,Mn)Te QUANTUM WELLS
Brown U n i v e r s i t y , P r o v i d e n c e , RI 0 2 9 1 2 , U.S.A.
* I n d i a n a U n i v e r s i t y , B l o o m i n g t o n , IN 47405, U.S.A.
* *
P u r d u e U n i v e r s i t y , W e s t L a f a y e t t e , IN 47907, U.S.A.
Les positions respectives des bandes et les energies d e liaison excitoniques sont etudiees dans les puits quantiques CdTe/(Cd,Mn)Te orientes selon (100) par spectroscopie d'excitation de la luminescence sous champ magnetique. Les decompositions des principales transitions excitoniques par effet Zeeman apportent des informations permettant l'etude theorique du role des excitons dans le cas ou les bandes electroniques ont un faible desalignment. La prise en compte de la contribution excitonique est cruciale pour determiner de facon precise les positions des bandes. Dans le cas d'une structure ayant une epaisseur de puits de CdTe de 50 A, et une concentration d'ions Mn x=0.24 dans la barriere, le rapport d e desalignment entre bandes de conduction et de valence est de 14: 1 environ.
Bandoffset and exciton binding energies are studied in (100) oriented CdTe/(Cd,Mn)Te multiple quantum wells by photoluminescence excitation spectroscopy in external magnetic fields. The measured large Zeeman splitting of the principal excitonic transitions provide input to a theory which addresses the role of excitons in the case of a small bandoffset. Proper inclusion of the exciton contribution is crucial to the accurate determination of the offset parameters. For the prototype sample of 50 A CdTe well widths and Mn-ion concentration x=0.24 in the barrier layers, the conduction-to-valence band offset ratio is found to be about 14: 1.
A number of semiconductor superlattice structures are emerging with wide gap 11-VI compounds such as CdTe and ZnSe as the quantum well material. From fundamental interest as well as for practica1 application, it is important to establish fundamental electronic parameters such as bandoffsets and exciton Coulomb energies in these new heterostructures. As for the former. there are suggestions from recent optical experiments that the valence band offset e.g. for the CdTe/(Cd,Mn)Te) and CdTe/ZnTe systems is particularly small [I]. At the same time, excitonic effects in these wide gap systems are large and must not be ignored if interband spectroscopy near the E gap forms the experimental basis for analysis. We have performed magneto-optical experikents to elucidate the offset question and excitonic binding in the CdTe/(Cd,Mn)Te multiple quantum well structures (MQW). The barrier material is a so-called diluted magnetic semiconductor (DMS) with 'giant' g-factors present at low lattice temperatures. This gives a significant experimental advantage in that the quantum well barrier heights can be substantially altered in a given sample by external fields to provide a wide basis of data for analysis without sample-to- sample uncertainties. However, in order to bring theory and experiment into agreement, it is critical to include properly the excitonic effects which, under conditions of a small valence bandoffset, add to the net potential well for the hole due to the electron Coulomb interaction. The final bandoffset by our determination is believed to be accurate to better than 10 meV; this makes the optical methods attractive when compared against e.g. photoemission methods.
In the elementary one electron and hole picture, Figure I depicts the iniluence of a magnetic field on a CdTe/(Cd,Mn)Te quantum well, assuming a rectangular well potential in the conduction and valence bands. We emphasize here the role of the 'heavy-hole' (lm.l=3/2 at k=O) valence states while noting that the light hole states are split from these to begin &ith at r-point due to the uniaxial component of the lattice mismatch strain (by about 35 meV for the sample discussed
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987579
C5-368 JOURNAL DE PHYSIQUE
below). The effect of the applied field is to alter the quantum well potential heights due to the spin splittings in the (Cd,Mn)Te barrier layers so that different effective potential barriers exist for the particular spin split electron and hole components. Circularly polarized optical transitions in Faraday geometry are also indicated in the figure.
We focus here on a particular CdTe/(Cd,Mn)Te MQW structure, grown in (001) orientation.
Strain induced effects in the (1 11) oriented structures are responsible for significant broadening of the ground state exciton resonances at Mn-concentration in excess of 10% so that precise spectroscopic determination of transition energies is difficult [2]. The sample was grown by MBE methods on a (001) GaAs substrate [3]. The MQW portion of the structure contained 30 periods of CdTe and (Cd,Mn)Te of x=0.24 with layer thickness ratio of 50A/96A. Photoluminescence excitation spectroscopy was performed in backscattering geometry with a low power tunable dye laser (P"I mW) loosely focussed on the samples. For unstrained bulk CdTe, the low temperature (excitonic) bandgap is at 1.5% e V and that for the alloy (x=0.24) is approximately 382 meV larger (see below for direct experimental determination of the latter in this sample). A 0.6% lattice constant mismatch is elastically accommodated with a moderate disclocation density and leads to finite strain adjustments to the bandgaps for the CdTe 'wells' and (Cd,Mn)Te 'barriers'.
Figure 2 shows portion of the excitation spectrum for the MQW sample at T= 2K in zero field (a). and in a field of 4 Tesla near the n=l exciton resonance (b) and (c). The two principal features in Fig. (la) are the HH and LH (light hole) excitons, respectively (with masses referred to the z-direction of the superlattice axis). The LH exciton transition is considerably broadened, presumably by the large penetration into the (Cd,Mn)Te barrier. In addition. we also obtained from the excitation spectra at higher photon energies the transitions for the n=2 HH exciton at 1.925 eV and that for the (Cd,Mn)Te alloy barrier at 1.990 eV. The barrier bandgap showed a resolvable but strongly broadened exciton transition typical of a mixed crystal; the value for this excitonic transition is subject to an uncertainty of +/- 5 meV. Nonetheless, this measurement is important since it gives the actual bandgap in the strained structure and can be directly used in quantum well calculations. Figure (lb) shows the splitting of the n=l HH exciton by 13 meV for the field in the direction of the superlattice axis (B ). This is also to the Faraday configuration and well defined circular polarization selection rulesZare obeyed. as indicated in the figure (which is actually a superposition of two excitation spectra obtained for opposite circular polarizations). In contrast. the LH exciton shows much weaker changes in this field geometry; however, with the field oriented in the layer plane, rather large splitting of the LH exciton was observed, approximately 17 meV in B =4 Tesla. in this geometry the HH splitting was reduced to less than 4 meV. The source for such f&ld anisotropy will be briefly discussed in section IV. In addition to the n=l HH Zeeman splitting.
both the n=2 HH and the ground state exciton at the barrier bandgap exhibited large splitting. For B =4 Tesla, the splitting for the former was A E 4 4 meV and for the latter A h 7 9 meV. The m%asured Zeeman splitting at the barrier bandgap was important in calibrating the observed magneto-optical effects for the quantum well transitions.
A summary of the n=l HH exciton splitting is shown in Fig. 3 as a function of the applied field (bottom panel). The figure also includes results of our calculations (solid lines) with specific bandoffset values and exciton binding energies described below. The splitting into lower and higher energy components was found to be asymmetrical for both n=l and n=2 HH excitons in the sense that the shift of the lower energy component always exceeded that of the high energy one (see e.g.
Fig. 4). This provides an important additional clue for characterizing the valence band offset and the exciton in this quantum well system.
We have used the experimental data as input to a calculation in the envelope function approach where the problem of an exciton in a DMS quantum well is solved by variational means [4] which differ in character from those applied e.g. for type I GaAs quantum wells. In wide gap 11-VI semiconductors, exciton binding energies are sizable. approximately 10 meV for bulk CdTe. In the context of a quantum well this means that the one particle envelope fungtions are %ore tightly bound than simply expected from the 'structural' quantum well potentials V (B) and Vo (B) in the conduction and valence bands, respectively. In our approach it is naturaq to consider effective confinement for the electron and the hole by 'effective'potentials V' and Vh which include the effects of Coulomb interaction and are used as additional variatgnal parameters. The proper inclusion of the Coulomb interaction is particularly important in the case where one of the bandoffsets is small since the more weakly confined particle is particularly susceptible for the Coulomb field in the z-direction. The exhange splitting of the conduction and valence band states where included into the starting Hamiltonian in a usual way for DMS materials. Details of our calculations will be found in [5].
... ,. ..
-1/2---'
---
v,"
- a, C1.65 1.70 1.75 1.80
----
1 r - - - \ - Photon Energy ceV I
* 1
I I
I 6 1 0'
-
: ! T B = F 4 T
Eg(CdMnTe)
C a, C
/2
... ... -
1.65, Photon Energy ceVl 1.70 1.75 1.80+ 3 / 2
... - ....-... ...-a - ...,... -
R y r e 1: Schematic of influence of magnetic field on the quantum well in electron-hole
-
representation .-
- =-.
V]-
a,,20- I I I
-
1.65 Photon Energy rev1 1.70 1.75 1.805
> 18- a-
Figure 2: Excitation spectra for the n=l HH and LH exciton in (a) zero field; (b) 4 Tesla field parallel to QW axis;
(5, and Q 4 Tesla field perpendicular to QW axis. T= 2K.
.s 14-
- 2 . a
10
-
-
a-3 -
E 5 :. -$
12
a
10
50 100
v,ll(mevl
s
- 5 :-
.-
# : 1.690
W B=JTt6)
-1 0
0 1 2 3 4 U=OT
Magnetic Field (T)
h 1.685 U=Jl'(o'J
Figure 3: (lower panel) Comparison of experiment (dots) and theory (with 25 meV
offset) for Zeeman splitting of the n=l .- HH exciton; upper panel: calulated field induced d 1.680
changes in exciton binding energy.
Figure 4: (lower panel) Calculation of exciton energy (interband energy with respect to CdTe bandgnp) as a.
function of valence band offset in zero and 4 Tesla O 50 100 field; Upper panel shows variations in the exciton
\:r
,,,a. lbinding energy. A 'best offset' of 25 meV is extracted by comparing with experiment.
C5-370 JOURNAL DE PHYSIQUE
The overall calculation is tested for a range of external magnetic fields and, when comparing with experiment, is therefore put to a rather stringent test as the fields employed in our experiments substantially modified the effective (valence) band potential well depth. As mentioned above, the bandgap of the (Cd,Mn)Te and its spin splitting (heavy-hole components) were directly obtained from experiments on the same quantum well sample. we used a ratio for the conduction to valence band exchange coefficients of 114 as obtained for bulk (Cd.Mn)Te (where N
a
= 220 meVand N
fl -
880 meV [6]). For the relative electron and hole effective masses we tookome=O.O% and m-0.8
for the z-direction whereas in the x-y layer plane mh-o.15 was used. Finally, E-9.7 forhe
was used.Figure 4 shows results of calculati~ns for the n=l HH exciton transition, used by us in part to determine the valence band offset V
.
The zero field and Zeeman splitting of the i n t e r p d transition (at B = 4 Tesla) are graphea as a function of the offset (lower panel) where a V in the range of 2 8 -30 meV matches quite well the experimentally observed splitting. Variation $ the exciton binding energy is also shown (top panel) for the same range of badoffsets. The figure displays the asymmetry in the amount of splitting into two components; this asymmetry is, however, considerably reduced from estimates based on the one particle picture and reflects the key role of Coy,lomb forces in a situation where one of the spin split HH cgmponents has only a very small V (i.e. a nearly type I1 quantum well). For this range of V the agreement for the Zeeman sp%tting of the n=2 HH transition is also quite good, are theOpredicted zero field positions for the n-1 and n=2 transitions. By taking the 'best' V = 25 meV and keeping all the variational parameters fixed, Figure 3 compares the theory with gperiment for the Zeeman splitting of the n=l HH exciton as a function of the magnetic field (lower panel). The rather good agreement serve as an additional demonstration of the consistency of our calculations. For the MQW structure in question, the conduction band offset is approximately 360 meV, reflecting a band offset ratio of about 14 to 1. Changes in the exciton binding energy in the external magnetic field were also naturally obtained from the calculations and upper panel in Figure 3 shows E,, for the lowest spin split n=l HH component. The case for the n=l LH exciton is more complicated as the large Zeeman splittings were obtained in a geometry where the direction of the magnetic field was perpendicular to the superlattice axis (Fig. 2c). This makes analysis of the data more complicated since the 1m.l can lo longer be used as good quantum numbers. The origin of the large field anisotropy for the L#I exciton (as well as the HH exciton) is. however, qualitatitavely clear, reflecting the combined action of the superlattice potential (quasi 2D hole) and uniaxial strains on the valence band states.Large field anisotropies have been previously encountered in bulk (Cd,Mn)Se, a wurtzite structure where crystal field effects split the valence band degeneracy at k=O and lead to uniaxial symmetry [7]. We have made rough calculations about the bandoffset for the light hole in the CdTe/(Cd,M%Te system and, while lacking the accuracy of the heavy hole case, find that the effective V is probably smaller than that for the HH particle. Accounting of the exciton interaction
bOy
the variational approach is subject to a larger uncertainty in this case as the hole is nearly unbound.The question of bandoffsets in semiconductor heterojunctions has been discussed recently from different experimental and theoretical viewpoints. The CdTe/(Cd,Mn)Te heterostmcture described here shows an offset in the valence band of this quantum well system which is less than 10% from that occurring in the conduction band. We have further experimental support also from recent measurements by Resonant Raman spectroscopy which involve the interacti n of excitons with
B
longitudinal optical phonons in this particular structure [8]. The value of V = 25 meV for the lm.l=3/2 valence band was obtained by putting the variational theory to rigorous test in a quantum well system where the bandoffsets are significantly altered by the applied magnetic field.
While the offset values thus obtained refer to a system where a moderate strain is present, we can make a crude extrapolation into the strain free limit by accounting for the uniaxial component of the lattice mismatch strain in the conventional way (the question of the role of the hydrostatic component of the strain is subject to a considerable uncertainty in a heterostructure as its accurate evaluation would imply precise knowledge about the absolute conduction and valence band energies of the entire system). For the (001) strain the HH-LH splitting at k=O is estimated to be- 25.4 meV in the CdTe layers and +13.6 meV in the (Cd,Mn)Te layers assuming a free standing superlattice. With such estimates we may crudely extrapolate (neglecting mixing of the lm.l=3/2 and lm.l=1/2 states) that inhthe 'strain-free' limit of the (001) CdTe/(Cd,Mn)Te heterojunctidn the net effkctive bandoffset V for the HH valence band in the square well model considered here is zero on the scale of 10 m % ~ . Similar conclusion is also reached for the LH band which is probably slightly type 11 in this limit.
Among the theories which have recently addressed the bandoffset question in semiconductor heterojunctions, there is some agreement that the so-called common anion rule has very little real basis for validity. For example, Tersoff [9] has presented results for a number of 11-VI compound
CdTe/(C%Mn)Te heterostructure a question can thus be raised as to the physical origin for such a small V in this system. The concentration of the hh-ion in the alloy barrier chosen here (x=
0.24) w% sufficiently high so that a fairly large electronic 'contrast' is present at the heterojunction (& " 400 mew. There are recent photemission measurements on bulk (Cd,Mn)Te alloys, including 8ork by Taniguchi et al [lo] which show that the position of the valence band maximum (VBM) is unaffected by the addition of
Mn
into CdTe within the accuracy of the experiment (presumably not better than some 50 mew. Some hybridization of the h4n-ion d-electron states with the valenec pstates does of course occur but, as these authors show. this has little influence on the VBM at k-0. One may therefore speculate that the experimental observation of a nearly zero band offset in the CdTe/(Cd.Mn)Te heterojunction implies the lack of any significant dipole effects at the heterointerfaces on the electronic states in question, perhaps reflecting specific dielectric similarities between Cd and h4n. In particular, when comparing our experimental results with the prediction by Tersoff for a zincblende CdTe,/MnTe junction [9], a sizeable discrepance appears.This work was supported by the DARPA/URI program.
References:
(1)
X.C.
Zhang, S.-K. Chang, A.V. Nurmikko, L.A. Kolodziejski. R.L. Gunshor. and S. Datk Phys.Rev. B31, 4056 (1985); J. Warnock. A. Petrou, R.N. Bicknell, N.C. Giles-Taylor. D.K. Banks. and J.F.
Schetzina. Phys. Rev. B32 8116 (1985); Y. Hefetz, D. Lee, A.V. Nurmikko, S. Sivananthan, X. Chu, and J.P. Faurie, Phys. Rev. B34, 4423 (1986)
(2) S.-K. Chang. A.V. Nurmikko. L.A. Kolodziejski, R.L. Gunshor. Phys. Rev. B33, 2589 (1986) (3) L.A. Kolodziejski. R.L. Gunshor. N. Otsuka X.C. Zhang. S.-K. Chang, and A.V. Nurmikko, Appl.
Phys. Lett. 47, 882 (1985)
(4) S.-K. Chang. A.V. Nurmikko, J.-W. Wu, L.A. Kolodziejski, R.L. Gunshor. Phys. Rev. B (to be published)
(5) J.-W. Wu and A.V. Nurmikko. Phys. Rev. B (to be published) (6) J.A. Gaj, R. Planel. and G. Fishman, Solid State Comm. 29. 435 (1979)
(7) R.L. Aggarwal. S.N. Jasperson. J. Stankiewicz, Y. Shapira. S. Foner, B. Khazai, and A. Wold, Phys. Rev. B28 6907 (1983)
(8) S.-K. Chang. A.V. Nurmikko. L.A. Kolodziejski, R.L. Gunshor. Appl. Phys. Lett. (in print) (9) J. Tersoff, Phys. Rev. Lett. 56. 2755 (1986)
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