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MAGNETOLUMINESCENCE OF n-TYPE ONE-SIDE-MODULATION-DOPED QUANTUM
WELLS
J. Orgonasi, J. Brum, C. Delalande, Gérald Bastard, T. Rötger, J. Maan, G.
Weimann, W. Schlapp
To cite this version:
J. Orgonasi, J. Brum, C. Delalande, Gérald Bastard, T. Rötger, et al.. MAGNETOLUMINESCENCE
OF n-TYPE ONE-SIDE-MODULATION-DOPED QUANTUM WELLS. Journal de Physique Collo-
ques, 1987, 48 (C5), pp.C5-407-C5-411. �10.1051/jphyscol:1987587�. �jpa-00226791�
MAGNETOLUMINESCENCE OF n-TYPE ONE-SIDE-MODULATION-DOPED QUANTUM WELLS
J. ORGONASI, J.A. BRUM, C. DELALANDE, G. BASTARD, T. ROTGER", J. C. MAAN' , G. WEIMANN* * and W. SCHLAPP* "
Groupe de Physique des Solides de l r E c O l e
ors sale
Superieure, 24, Rue Lhomond, F-75231 Paris Cedex 05, Franceax-~lanck-~nstitut, Hochfeld Magnetlabor, B.P. 166X, F-38042 Grenoble, France
* * ~ o r s c h u n g s i n s t i t u t der Deutschen Bundespost, 0-6100 Darmstadt, F.R.G.
RCsumC: Nous rendons compte d'expbriences de photoluminescence & basse tempkrature (2 K) sur des puits quantiques, GaAs-Ga(A1)As
B
modulation de dopage, dans des champs magnetiques allant jusqu'h 20 T. La cornparaison entre la thhrie et 1'expCrience rkvde le fort couplage entre les bandes de valence, des oscillations surprenantes sont observCes sur l'bnergie des transitions de basse Cnergie.A b s t r a c t : We report magnetoluminescence experiments in a one-side-modulation-doped quantum well performed at 2 K in field up to 20 T. A comparison between calculations and experiments, points out the strong coupling between the valence subbands. Surprising oscillations are observed on lower lying transitions.
The problem of valence subband dispersion in the plane perpendicular to the growth axis z in quantum wells is of some interest because of the expected strong coupling between heavy and light hole subbands at k,,y#O. Dispersion curves have been calculated in GaAs-Ga(A1)As systems [I-41, and cyclotron resonance [5] and magneto-transport experiments [6] in p-doped QW have been carried out to check these results. They pointed out the strong coupling between hole levels, the lifting of the Kramers degeneracy, and the existence of many-body effects. Magneto-optical measurements of the exciton binding energy in undoped GaAs-Ga(A1)As QW [7] proved the complexity of the valence band too. But in such systems, the luminescence involves only the first conduction and valence Landau level, because of the relaxation of carriers towards band edges, and the excitation spectroscopy evidences very complex structures quite difficult to explain. On the contrary in n-type
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987587
C5-408 JOURNAL DE PHYSIQUE
modulation doped quantum wells (MDQW) transitions occurs between all the Landau levels located in the Fermi sea and the populated hole levels. Provided the excitation is sufficiently intense to thermally populate many hole levels, many lines can be observed in photoluminescence spectra. Because of the negligible binding energies of excitons in such plasmas [8], we interpret the photoluminescence lines as band-to-band transitions, and a comparison of the data with a calculation is possible, taking account the band gap renormalization.
We performed our photoluminescence experiments, in a n-type 150
A
thick one-side MDQW. The GaAs well is followed by an undoped 330 A-thick Ga0.61A10.39A~ spacer layer, and a 300 A-thick Si-doped part ( ~ = 4 x 1 0 ~ * ~ m - ~ ) . As explained e.g. in [4], this structure improves the quality of the GaAsIGa(A1)As inverted interface, and thus the mobility of the GaAs channel.Magnetoluminescence experiments were performed at 2 K in magnetic field up to 10 T, and then in field up to 20 T, in the Faraday configuration. A typical spectrum recorded at B=7.5 T with a o+analyser is shown in fig 1. Peaks are indicated with arrows, they correspond to high energy transitions related to electron-hole recombinations. We have plotted the energy of the photoluminescence peaks as a function of the magnetic field for o+ (crosses) and d (circles) polarization as shown on fig 2 and 4.
A self consistent Hartree calculation [9] carried out up to 10 T allow us to qualitatively explain these data. Assuming a parabolic conduction band and an axial approximation for the Luttinger Hamiltonian which describe the valence band, we can label the energy levels by an index n and the value of the spin S[l]. We obtain for the first conduction band:
where, oc and pB are respectively the cyclotron frequency and the Bohr magneton, S=+1/2 the electron spin. The electron mass and the Land6 factor g* are taken equal to 0.07m0 and -0.4 respectively. Thus the electron levels y;f2 and y i 1 i 2 are respectively labeled:
n=-1,0,1
...
for spin up levels S=+1/2 and n=0,1,2...
for spin down levels S=-112. The hole bands are much more difficult to describe because of the coupling between light and heavy holes at B d . We label yn@ the two sets of Landau levels which correspond to the first heavy hole bound states HH1 at B-0; they still remain essentially heavy hole levels at BzO, and Yna andy n P
are respectively mJ=-312 and mJ=+3/2 states at B=O. For comparison with experiment we note that statesp
are quasi harmonic (see fig 3 ) and so less perturbed by the coupling than the set a (except for the n=-2 level which,in the set a, is an uncoupled one).Because of the selection rule A n d l and the remarkable quasi-harmonicity of the
v n l b ~ n + l P
electronic to hole level transitions which have a dt polarization, it is easy to recognize them. They are shown on the right part of fig 2 by crosses (experimental data) and continuous lines (theory). Then, the attribution of the y;112+~n-la transitions becomes easier. The fit of these lines is shown on the right part of fig 2 (continuous lines).
The other transitions are found to be recombinations induced by the heavy and light hole coupling. TheyThe calculations are thus in very good agreement with our experimental results.
We present in fig 4 the results of another magnetoluminescence experiment performed in the same experimental conditions. It clearly shows the sudden disappearance of several luminescence lines at 20,8,5.3,4,2.8 T respectively.These lines fade away due to the depopulation of the initial conduction states. For a perfect heterostructure and a vanishing electronic temperature T,, this should occur any time a conduction Landau level pops out the Fermi sea. In fact assuming a fixed electron concentration ( n , = 4 . 5 ~ 1 0 ~ ~ c m - ~ ) and Te=O K, the calculated B values beyond which only 1 ,2 ,3 ,4 and 5 conduction Landau levels are found below the Fermi sea are 18 ,9 ,6 ,4.5 and 3 T. These values roughly correspond to the experimental results, the discrepancies being likely associated with broadening and finite temperature effects.
The oscillations exhibited by the energies of the two lowest lying PL lines
vo1J2+~ 1P
andv-1-112+~-2a
when B increases are more striking since these lines involve initial states which are always populated (v-1-112 becoming depopulated only near 18 T).Irrespective of the exact B-dependent motion of the chemical potential p, when an excited Landau level intersects
+,
one would not expectifnS
is constant any change in the energies of these levels: both the recombining electrons and holes have their energies which are only dependent upon n,. Thus, the oscillations of these two transitions energies which are centered at 17, 9, 5.6 and 3 T (see fig. 4) result either from complicated B-dependent many-body corrections to the Hartree terms, or rather from fluctuations of the transferred electron concentration in the QW any time the chemical potential intersects the highly singular Landau levels density of states. Such an oscillatory change in ns would occur if for instance the chemical potential is held fixed ( by some large reservoir outside the QW e.g. the Ga(A1)As donors or the GaAs depletion charges).In conclusion, we have reported magneto-luminescence experiments from 0 up to 20 T and presented a fit of our experimental data to theory which takes into account the strong coupling between light and heavy holes. The observed oscillations of the lowest lying PL lines are interpreted as fluctuations of the eIectron concentration in the well as the Landau levels cross the Fermi sea. Other precise experiments should be carried out to check this assumption.
References
[I] M. Altarelli, Proceedings of the Les Houches Winterschool on Semiconductor Superlattices and Heterojunctions, 1985 (Springer-Verlag, Berlin).
[23 T. Ando, J. Phys. Soc. .Tap. 1528 (1985).
[3] D.A. Broido and L.J. Sham; Phys. Rev. B a , 888 (1985).
141 M.H. Meynadier, J. Orgonasi, C. Delalande, J.A. Brum, G. Bastard, M. Voos, G. Weiman and W. Schlapp, Phys. Rev. B s , 2482 (1986).
[5] H.L. Stormer, Z. Schlesinger, A. Chang. D.C. Tsui, A.C. Gossard, and W. Wiegmann, Phys. Rev. Lett. 3 , 2 5 7 9 (1984).
[6] J.P. Eisenstein, H.L. Stormer, A. Chang D.C. Tsui, A.C. Gossard, and W. Wiegman, Phys. Rev. Lett.
51,
2579 (1984).C5-410 JOURNAL DE PHYSIQUE [7] J.C. Maan, G. Belle, A. Fasolino, M. Altarelli, and K. Ploog,
Phys.Rev. B a , 2253(1984).
[8] D.A. Kleinmann, Phys. Rev. B a , 3766 (1985).
191 C. Delalande, J.A. Brum, J. Orgonasi, M.H. Meynadier, G. Bastard, J.C. Maan, G. Weimann and W. Schlapp, Superlattices and Microstructures, Vo1.3, No. 1,1987.
ENERGY ( meV
r t g 8 1 ~ l l 1 1 1 1 1 1 1 1 1 ~ 1 1 1 ~ J
0 5 10 0 5 10
B (Tesla B (Tesla
FIG 1: 6 photolunlinescence spectrum recorded at B=7.5 Teslas and T=2 K.
FIG 2: Comparison between the experimental (crosses and circles) and theoritical (curves) values of the interband magneto-optical transitions up to 10 Teslas. The and Y have been omitted and spin
1'
andk
mean S=+1/2 (see text).10 I
t q t ; , I #,&i
1 a5 o 5 10
kl (X x lo6 ern-') B (Tesla
FIG 3: Calculated in-plane dispersion curves (left part of the figure) and Landau levels (right part of the figure) of the valence band in the 150 i( MDQW. The two dispersion curves and the two sets of Landau levels converging towards the fundamental HHl 'heavy hole state are separated for clarity.
FIG 4: Magnetoluminescence fan chart for o+ (crosses) and CJ- (circles) polarizations.
I I I I I l l l I f 1 l I I I I l I l
0 5 10 15 20
