CALCULATION OF THE CIRCULAR POLARIZATION OF QUANTUM WELL PHOTOLUMINESCENCE

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CALCULATION OF THE CIRCULAR POLARIZATION OF QUANTUM WELL

PHOTOLUMINESCENCE

A. Twardowski, C. Hermann

To cite this version:

A. Twardowski, C. Hermann. CALCULATION OF THE CIRCULAR POLARIZATION OF QUAN-

TUM WELL PHOTOLUMINESCENCE. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-211-

C5-214. �10.1051/jphyscol:1987543�. �jpa-00226747�

CALCULATION OF THE CIRCULAR POLARIZATION OF QUANTUM WELL PHOTOLUMINESCENCE

A. TWARDOWSKI and C. HERMANN*

~nstitute' of Experimental Physics, The University of Warsaw, Hoza 69, PL-00681 Warsaw, Poland

" ~ a b o r a t o i r e de Physique de la Matiere ~ o n d e n s 6 e ( l ) , Ecole Polytechnique, F-91128 Palaiseau Cedex, France

RESUME

On prBsente un calcul de la luminescence polarisee de puits quantiques excites en lurniere polarisbe circulaire, qui pour la premiere fois prend en cornpte la structure cornplexe des bandes de valence. L' analyse des spectres d'excitation publies pour le systhrne All -,Ga,As/GaAs montre I'importance des effets excitoniques et de la relaxation du spin Blectronique.

ABSTRACT

We present the first calculation of All -,Ga,As/GaAs quantum wells photoluminescence polarization under circularly polarized excitation, taking into account the complex structure of theQW valence band. A careful analysis of the published excitation spectra on the All-,GaXAsl GaAs system stresses the importance of excitonic effects and electron spin relaxation.

The identification of heavy- and light-hole quantized levels in All-,GaxAs/GaAs quantum wells (QW) or superlattices is currently done by studyinp the photoluminescence excitation spectrum

o INTENSITY (arb. u.) of the structure under U a r l v o+polarized

f

_o

-

illumination (1). This technique greatly

rn enhances the structures as compared to

X

e +

unpolarized excitation. In this so-called "optical

2 % -

pumping" situation the light helicity is

Si

transferred to the solid through spin

2 , orientation of the promoted electrons (2). This

r

p -

leads to a circular polarization P of the

rn luminescence, defined by

R P = (I+

-

^{I-) I (I+}

+

I-),

$$ -

CD where I+ (resp. I-) is the o+ (resp. o-) circularly

- c

polarized luminescence intensity for a given

7' m

,

^I

m circularly polarized excitation. In a QW polarized

+ +

? ? o excitation spectrum, an increase (decrease) in

o FJ i

POLARIZATION polarization is considered as the hall-mark of Fig.1: Excitation spectrum of the circular the onset of a transition originating from a photoluminescence (1+,1-) and its polarization heavy (light) hole levet. Indeed, the published

spectra (3-6), always similar to the one in Fig. 1, On

a

46-peri0ds ( present a high polarization P for near bandgap A10.3Ga0.7Asl54A GaAs), after Ref.3.

(l)Groupe de Recherche du Centre National de la Recherche Scientifique

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987543

C5-212 JOURNAL DE PHYSIQUE

excitation, followed by a negative or zero dip for larger excitation energies hv. Since the heavy hole and light hole states are decoupled in the wells, a +loo% polarization is predicted for the 1 hc transition between the n = 1 heavy hole and conduction levels (7), and a -100% polarization for the l l c contribution (n = 1 light hole to conduction transition) (5). This leads to the identification of the dip of the P(hv) curve with the onset of the light hole transition for hv = Ellc.

However when the simplest parabolic model of decoupled QW valence bands is used to obtain the weigths of the transitions, the net polarization remains positive for all excitation energies : P=+100% for the 1 hc transition and P =+60% at hv = Ellc (6), in contrast with the experimental resuRs.We present here the first calculation of P which takes into account the coupling of the QW valence bands, and predict a variation in qualitative agreement with the experiments. An analysis of the published data on the AI1,GaxAs/GaAs system emphasizes the importance of excitonic effects and electron spin relaxation.

11. POLARIZATION OF PHOTOLUMINESCENCE The considered process is the following (see fig. 2):

i) Excitation of electrons from valence subbands into the lowest (Ic) conduction subband.

ii) Energy relaxation of photocreated electrons and holes to the bottom of the conduction

subband and the top of the I h subband, respectively.

iii) Recombination of thermalized electrons and holes.

Since the P(hv) spectra show up a strong variation, this implies the presence of electron and/or hole spin relaxation: otherwise, the recombination would be the exact reverse process of the absorption, and the luminescence would always be +100% polarized. In bulk solids the p-type valence wave function is more affected by spin relaxation than the s-like conduction

t

wave function (2).Here a smaller hole spin relaxation is

2

expected due to the lifting of the valence band

W

z

degeneracy. In our calculation we take the extreme

W hypotheses of complete

Jxde

spin relaxation, and zero

spin depotarization in the conduction band. We shall consider band-to-band transitions in intrinsic samples.

For o + (respectively o-) light excitation the density operator pfexc describes the state of photoexcited electrons and reads

P

*

exc

' xi

PP+

1

Wi ><Wi

I

^PP+

where p* is the dipole transition operator for o+ and o- light and

1

^{yi >} are the initial valence states fbom which

WAVEVECTOR k//

the electrons were promoted. The summation is performed over the different valence subbands Fig.2: Schematic band structure and compatible with energy conservation in the absorption schemes discussed in

9

II* process and over all thedirections of the layer plane

offset parameter, i.e. the well depth, influences the P(hv) shape through the JDOS for the 11 transition : the shallower the well, the smaller the JDOS and the less negative the polarization for hv = Ellc. The same calculation as in fig.3 with QC=0.85 yields a minimum polarization of

+

13%.

Ill. COMPARISON WITH EXPERIMENTAL RESULTS

The present calculation reproduces the overall variation of P(hv). The inclusion of a damping JDOS 's for the considered transitions.

The recombination into thelh valence subband is 10

z 0

-

-

described by similar density operators pfrec. Then the o+,d luminescence intensities (under o'excitation) are deduced :

I+ = Tr p+,reat

.

pkrec

and the luminescence polarization P is obtained.

Figure 3 shows the result of such a calculation versus ::the excitation photon energy hv for a

A10.21Ga0.79A~IGaAs quantum well, L = ~ ~ o A , obtained in the axial approximation, i.e. assuming an isotropic heavy hole dispersion in the layer plane and for an offset parameter Qc=0.57.The eigenenergies and wave functions are obtained by a variational calculation

~ l ~ l l ~ ~ l l l l', l , ~

-

which uses the bound states for k// =O as a basis for l l l r

154 t- 4

o

4 B

-10

^ ₃ ^80- cd 20';

V V)

5:

f- l o -

4 z

15' the

k//

+4 situation (8). The main feature of the energy EXC'TAT'oN ( eV ) dispersion is a strong coupling between the subbands, Fig.3: Excitation spectrumof the lumi- resulting in characteristic nOn- parabolicities as nescence circular polarization and schematized in fig.2. In particular the second hole JDOSS for the different transitions, subband has an electron-like effective mass for small for the A10~27Ga0.79A~IGaAs QW k// and a hole-like mass for k//lx/L. This band is 2h described in $11. The arrows denote for an infinite well and I I for a narrow enough wel1,and in the onsets of transitions between the data on the AI1-xGaxAs/GaAs system (3-6) its type is quantized levels. always 11 (8). Its negative mass for small

k//

leads to a high JDOS for the optical transition between this band and the conduction band. We verified that in the range of k// in fig. 3 our valence energy dispersion does not differ much from the extended calculation of Altarelli et al. (10). In the energy range hv<E1lc only electrons from thelh valence subband, with a dominant heavy hole character, are excited into the conduction band: the resulting photoluminescence polarization is thus close to

+

100%. For an excitation energy exceeding E l lc the electrons from the 1 I subband, carrying a -100% polarization, start to contribute to the luminescence. The JDOS for this transition is very high, resulting in a total negative polarization as strong as -78%. The contribution of the n = 2h to n = l c transition is very weak, as it is parity forbidden for Iy/=O. The

-

..

C5-214 JOURNAL DE PHYSIQUE

parameter, which modelizes the sample inhomogeneities, as small as 0.2 meV, reduces the large negative dip of P(El lc) to zero, in better agreement with the data. However two experimental features are not accounted for :

i) The total luminescence intensky excitation spectrum I+

+

^I- evidences strong heavy- and light-hole excitonic peaks in the JDOS (see fig.l), in contradiction with the step-like calculated JDOS for hv<El lc.

ii) Electron spin depolarization occurs both during energy relaxation stage and in the thermalized state.

By comparing the intensity and polarization excitation spectra for hv=El lc one can separate the contributions of electrons originating from 1 h and 11 valence subbands. At hv = Ellc the former ones are more depolarized, which favours the negative contribution of the I l c transition.ln the reported data (3-6) on samples with different compositions, geometries and exciton intensities, the dip of P(hv) varies in a relatively small range (-10%

+

0%). This suggests an intrinsic spin relaxation mechanism : the longer collision time in bidimensional structures should make the D'yakonov-Perel' process (1 1) efficient even at relatively small kinetic energies.

In conclusion, the polarized excitation spectra have currently been used in AI1-xGaxAslGaAs OW'S spectroscopy, and should be useful to deduce parameters of the lnP/Ga0.471n0.53As system.ln fact their understanding requires the inclusion of the valence band complexicity, and of excitonic effects. These data also evidence efficient spin relaxation in the conduction band of layer systems.

ACKNOWLEDGMENTS

We thank Dr G. Lampel and Dr D. Paget for a critical reading of the manuscript.

REFERENCES

(1) See the review paper by R.C. Miller and D.A. Kleinman, J. of Luminescence

32,

520 (1985).

(2) G. Lampel , Proceedings of 12th International Conference on the Physics of Semiconductors, Stuttgart 1974, ed. M.H. Pilkuhn (Teubner, Stuttgart 1974) p. 743.

(3) R.C. Miller, D.A. Kleinman and A.C. Gossard, Proceedings of 14th lnternational Conference on the Physics of Semiconductors, Edinburgh 1978, Inst. Phys. Conf. Ser. Nr 43, 1043 (1979).

(4) W.T. Masselink, Y.L. Sun, R. Fischer, T.J. Drummond, Y.C. Chang, M.V. Klein and H. Morko~, J. Vac. Sci. Technol. &,I 17 (1984).

(5) C. Weisbuch, R.C. Miller, R. Dingle, A.C. Gossard and W. Wiegman, Solid State Commun.

Z ,

219 (1981).

(6) R. Houdr6, These de I'Universite Paris-Sud, Orsay (1985).

(7) The quantized levels are labelled according to their character at zero kinetic energy.

(8) A. Twardowski and C. Hermann, Phys. Rev.B, 15 May 1987.

(9) In the InPIGao~471n0.53A~ system, the second valence subband may be 2h or 1 I according to the well width and the offset parameter.Pc0 is predicted for hv = El lc only in the latter case.

(10) M. Altarelli, U.Ekenberg and A. Fasolino, Phys. Rev.

Kg,

5138 (1985)

.

(11) M.I. D'yakonov and V.I. Perel', Sov. Phys. JETP

33,

1053 (1971) [Zh. Eksp. Teor. Fit.

522,

1954 (1971)l.