High magnetic field effects on the dynamics of excitons in a GaAs quantum well

~ ) Pergamon Solid-State Electronics Vol. 37, Nos 4-6, pp. 923-928, 1994 Copyright ~? 1994 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 0038-1101/94 $6 .00+0.00

HIGH MAGNETIC FIELD EFFECTS ON THE DYNAMICS OF EXCITONS IN A GaAs QUANTUM WELL

S. HAACKE 1, A. P. HEBERLE 2, M. POTEMSKI 1, J. C. MAAN 3, W. W. ROHLE 2 and G. WEIMANN 4

~Grenoble High Magnetic Field Laboratory, MP1F/CNRS, B.P. 166, 38042 Grenoble, France, 2Max- Planck-lnstitut f. Festkrrperforschung, Heisenbergstr. I, 70569 Stuttgart, Germany, ~High Field Magnet Laboratory, University of Nijmegen, 6525 ED Nijmegen, The Netherlands and 4Walter-Schottky-lnstitut,

Techn. Universit/it M~nchen, 85748 Garching, Germany

Abstract--The time-resolved photoluminescence of excitons in a 9 nm GaAs/(AI.Ga)As quantum well structure under high magnetic fields (B ~< 21 T) applied along the growth direction is reported. Magnetoex- citons related to the lowest light-hole subband with a well defined orientation of the magnetic moment are selectively excited. The tbermalisation between the two Zeeman split 1 s heavy-hole exciton ground states is found to be accelerated by the magnetic field. Moreover, a decrease of the PL rise-time is observed with respect to the zero field case where light-hole excitons and the electron heavy-hole continuum states are simultaneously excited.

INTRODUCTION

The energy diagram of quantum well (QW) excitons under high magnetic fields has been intensively studied in recent years by steady-state photoluminescence (PL) but far fewer experiments have focussed on the dynamics of magnetoexcitons. Absorption spectra taken with the magnetic field parallel to the growth direction show discrete peaks associated with magnetoexcitons and a disappearance of any free-carrier continuum. Such a modified energy spectrum is thought to change the dynamics of magneto-excitons when, for instance, thermalization processes are im- portant. Moreover, magneto-excitons are spin-split by the Zeeman effect according to their different orientation of magnetic moment (Ms = + 1). Steady- state PL experiments have suggested that the conservation of Ms during the relaxation from the excited states to the 1 s ground state is favoured with increasing magnetic field and that the Ms-relaxation time between the two 1 s heavy-hole magneto-excitons with opposite M s is comparable to the excitonic radiative lifetime[l].

At zero magnetic field the dynamics of QW excitons have attracted great interest[2, 3], especially concerning the presumed enhanced radiative recombination due to the size confinement of excitons in QW's[4]. Magnetic moment relaxation times of 50-150ps depending on the excitation density have recently been found for excitons at zero field[5].

High magnetic fields allow to excite excitonic states of a well defined magnetic moment selectively by adjusting the laser energy and polarization to a given magneto-excitonic resonance, and to study the carrier dynamics in such a situation. Assuming a time-inde- pendent radiative lifetime at any moment, the photoluminescence (PL) intensity is proportional to the population of the magneto-excitons. The aim of the

present paper is to investigate the relaxation processes between the two lowest Zeeman-split heavy- hole magnetoexcitons implying a reversal of the magnetic moment by recording their PL decay. The PL rise gives information about the relaxation processes between the excited and the luminescent exciton state.

EXPERIMENTAL ASPECTS

The sample investigated consists of three GaAs QW's of 90 A thickness sandwiched between A1026Ga074As barriers grown on an undoped (100) GaAs substrate. A large barrier thickness (1000 A,) allows us to consider the GaAs layers as decoupled single QW's.

The cw experiments have been carried out with a conventional PL set-up using a Ti:sapphire laser (2---720--840 nm) pumped by an Ar-ion laser. A spectral resolution of 1 A, (0.2 meV) is provided by a 1.5 m-monochromator.

For the time-resolved studies a Styryl 8 dye laser (2 = 730°820 nm, autocorrelation pulse width 7-8 ps) synchronously pumped by a mode-locked Nd:YAG laser (v = 76 MHz) was used. A two-dimensional synchroscan streak camera in conjunction with a 0.32 m-monochromator was used in order to obtain a simultaneous recording of time- and energy-resolved PL spectra. The spectral and temporal resol- utions are of 0.5meV and 15-25ps, respectively. Deviations of the electron beam in the streak camera by the stray magnetic field in the wavelength axis were corrected by recalibration for each magnetic field. The effect on the time-axis was negligible. The sample was placed in a He bath cryostat (T ~< 2 K) mounted in the centre of a 21 T resistive magnet with the magnetic field and the exciting laser beam parallel

923

924 S. HAACKE et al.

to the QW growth direction (Faraday configuration). Achromatic )./4 plates and polarizers allowed to generate and to detect light of circular polarisation.

STEADY-STATE RESULTS

For zero magnetic field the luminescence spectra at T = 2 K show two transitions related to the 9 nm QW's at 1.550-1.555 eV separated by 1 meV and with a narrow line width of 1-1.5 meV (excitation density ~50W/cm 2, inset Fig. l(a)). The excitation spectra reveal a quite small Stokes shift of 1.3 meV with respect to the high energy PL peak. The dependence of the relative intensities of both transitions on the excitation density enables us to identify the high energy transition as the free (e~, hhl)-exciton, the low energy transition being attributed to localized exciton states saturated by high excitation densities. For magnetic fields BI~ >/10 T four transitions--two pairs of two transitions with opposite polarisation----can be

4 --

2 --

0 1.550

1.555

(a) 10

d e t -

- - - d e t +

-- B

B = 14T 5

A'

|

I |

I A 0 I ,L | tl 1.545 I

I

I

I I

1.555 1.560

Energy (eV)

4

.d

[ f 1.565 1.570

(b)

i~ E 2 ~ E1 ~ Is(el , lhl)

"~RB I X~RA

,,0,m l S A B' " . . . . . . . . . . . . "~t~.e~m

L o c a l i z e d • A '

s t a t e s

Fig. I. (a) Steady-state PL spectra at B~ = 14T under excitation of the light-hole level E 2 showing the four main transitions B, A, B', and A'. Inset: Steady-state PL spectrum at B~[ = 0 T. (b) Representation of the excited 1 s light-hole levels El and E2, the heavy-hole 1 s ground states A and B and the respective localized states A' and B'. The different relaxation channels with the corresponding lifetimes are

indicated (see text).

resolved (Fig. l(a)). Both high energy transitions can be identified as the Zeeman split excitonic transitions (labelled excitons A and B) with opposite magnetic moment M s = I + l ) for the tr ~ and M s = [ - I) for the a - polarised transition following a diamagnetic shift with increasing B~:. The two localized transitions are labelled A'(a *) and B'/(tr - ) , respectively.

Excited magnetoexciton states have been probed by PL excitation (PLE) spectroscopy[l]. At 10meV above the 1 s state of the (et, hh~)-exciton one can distinguish the 1 s state of the light-hole (e~, Iht )-exciton showing a diamagnetic shift. For magnetic fields BI! > 5 T the excited states of the heavy-hole exciton (2s, 3s . . . . ) appear at higher energies than the I s light-hole exciton with a more or less linear field dependence. It should be stressed that for B. > 12 T and due to the narrow PLE linewidths (~,1 meV), magnetoexcitons of well defined magnetic moment can be selectively excited by tuning the laser energy resonant to the corresponding transition. As an example, Fig. l(a) displays the a + and a polarised PL spectra at B = 14T for an excitation of the Ms = I+ 1) component of the 1 s light-hole state (E, in Fig. l(b)). The most striking feature of Fig. l(a) is the fact that the excitonic high energy peak B is roughly twice as big as peak A. With the reasonable assumption that A and B have the same probability for radiative recombination, it follows that A and B are not thermalized, i.e. their respective populations hA, na do not follow a Boltzmann law n~/nA = exp[( -AE/kT L)], with AE the energy separ- ation (1.2 meV), and the lattice temperature T L (2 K). The preferential population of exciton B is due to the fact that is has the same electronic spin direction as the excited (et, lh~) exciton component. The obser- vation of a non-thermal population ofexcitons A and B under cw excitation has indicated that the magnetic moment reversal time between the exciton B and A is of the same order of magnitude than the radiative lifetime[l]. In a similar way, exciton A can be made dominant with an excitation energy resonant to the Ms = I - I) low energy component of the 1 s (e~, lhj ) exciton (labelled El).

Increasing the magnetic field leads to an increase of the intensity radio B/A (excitation of E2). This intensity ratio will be followed in the time-resolved experiments as a function of the magnetic field.

PICOSECOND PL

Before we discuss the results of the time-resolved luminescence we will summarise the relaxation processes that govern the exciton dynamics (see Fig. l(b)).

1. Relaxation from the excited light-hole state (either E~ or E2) down to the heavy-hole excitons A and B. Due to an energy difference of 10-11meV, emission of acoustical phonons is expected to be the relevant relaxation process. When exciting in E2 relaxation to A with the lifetime r•A requires

Excitons in a GaAs quantum well

5 [ - (a) o d ~ . • B' (1562.5 meV) / ° " ~ • A' (1560.5 meV) | ° , ~ . e ' ~ b , , ~ _ " A (1564.1 meV) / , v / r . ~ ~ q h ~ , ~ . o B (1566.1 meV)

• _~ / ~ _ ~ ~ ',.,,,.'...... " " ~ " . " . ? , . , , ~ . / "," ~ \ c Do ~ - " "_, ,, "' ~ " " " . ' I . . ' , .

oJ | I3 • •

l \ °¢

.a 2 t,a" .',o ° o °

~' °o

| : - 1 I I 1 t I

-'-" 4

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-- "11 ( b ) . . a ~ s ~ • B (1566.1 meV)

i f - " ~ o A (1564.1 meV) n" ~ " A' (1560.5 meV)

• , , ~ " ~ * ~ I L . _ o B' (1562.5 meV)

_ o ~ . . ~ '%oo' : 'o v ' ~ - - . : . . - . ~ o " o - , " ~ 'o-O°~ ~ " . ' ~ " . " . " . ~ . . . . ~ . ~ B o

, , ~o~ ~ ~ • . - ~ , , . , , : - , o ~ . . ' : OOOo~ o % ~ ' ' . ' . . . " . ~ . . . .

. o o o o e • • • • v o O o o o o o o, .. ; °

o v ° ~ o o o o o o •

~ . ~ o o ° o ° OOoo~Ooo o . . ~ . o . . o o o o o • oo°~_ °

v Or• O O O uO'O • o v °° oo o

o o 0 0

~8° ° I I I o I I 0 200 400 600 800

Time (ps)

Fig. 2. (a) Transients of the PL transitions B, A, B', and A' at 21 T under excitation of E2 (semi-log. scale). Note the fast decay slopes ¢, of exciton A and B. (b) The same transients at 21 T under excitation of E,.

Exciton A shows the same decay behaviour as in (a).

925

reversal of the electron spin (see Fig. l(b)). Relax- ation down to B conserves the spin (lifetime zRs).

2. Relaxation from exciton B to A implying reversal of the spin of both electron and heavy-hole is characterized by a lifetime %. The energy separ- ation between both excitons can amount to 2 meV at B H = 21 T. The relaxation therefore requires emission of acoustical phonons.

3. Relaxation from the B or A exciton to the corresponding localized state B' and A' , respectively with a lifetime ~th~m"

The PL decay rate of exciton B is the sum of I/zs + l/'~therm "+" l/Zrdd ('rrad being the radiative exciton lifetime) whereas process l determines the PL rise- time.

A decay behaviour with two characteristic decay times is observed for the B exciton when the excitation energy coincides with the E2 light-hole exciton state. In this excitation condition the B exciton is twice as intense as the A exciton in the cw spectra. The time-resolved data have been obtained under excitation conditions such that the time-integrated


spectra are equivalent to the cw results. The mean exciton density is estimated to be 10 ~° cm-:. The time evolution of the four PL transitions B. A. B'. and A' at B~: =21 T is displayed in Fig. 2(a). Note the dominance (by a factor of 10) of the B exciton during the first 120 ps. After a rapid decay with a lifetime T~, the B exciton shows the same decay than the A, A' and B' levels with a longer lifetime r 2 = 180-200 ps. The two slopes show a different dependence on the magnetic field. For B~r/> 12 T a clear decrease of the z~ time can be observed. In fact, from the zero field value of r] (B = 0)= 180+ 5 ps the decay time decreases down to z~ =44__+2ps at Bl~---21 T. This two-component decay behaviour can be understood by looking at the other transitions represented in Fig. 2(a). The localized states (A" and B') show a monoexponential decay with a slope T of the same value than T:. Apparently, for longer times (t > 300 ps) the exciton B and the localized states A' and B' are in thermal equilibrium, which means, for A' as an example, that the ratio of the populations (riB, hA, ) is determined by a carrier temperature T c following nB/n ̂ = e x p [ - ( A E B _ A , / k T c ) ]. The shorter decay z~ can thus be interpreted as a relaxation time from the exciton B to all low-energy states, i.e. exciton A (with the lifetime Zs) and the localized states A' and B' (lifetime Z~h,~m).

In the opposite excitation condition when the light-hole E~ level is excited selectively, the exciton A is preferentially populated and the high energy exciton B is roughly one order of magnitude smaller than the A luminescence. The temporal behaviour of the four PL lines is depicted in Fig. 2(b) for BII = 21 T. The A exciton shows two decay times (z~, ~2) much like the B exciton in the excitation condition dis- cussed above. It is interesting to note that the z~ decay time of exciton A is the same (95 ps) here than under excitation of the E2 level confirming the interpretation of this time as a thermalization time with the localized states.

In Fig. 3(a) the ratio B/A of the PL transients is depicted on a logarithmic scale for different magnetic field values. With the reasonable assumption that both excitons have the same recombination probability, the intensity ratio is a direct measure of the ratio of exciton population l ( t ) = nB/nA(t) . Figure 3(a) shows a dominance of B excitons with respect to A by a factor I 0 ~ 10-20 immediately after the laser pulse (t ~- 0) confirming the interpretation of the cw spectra that ~'RB <~ TRA when the E: level is excited. The following thermalization process between the populations of B and A is characterized by an exponential decay with an inverse slope of ~ = 5 2 + 3 p s at BI.. = 21 T. For t >/250 ps an equilibrium situation is reached with a temperature of T c ~ 18 K. The dominance of the B exciton in the cw spectra can now be explained by the preferential population of B at short times. For lower values of the magnetic field the excess population ratio I0 at t = 0 decreases with respect to the equilibrium value I X at long times (see

Fig. 3(b)). That is the reason for the decrease of the B/A intensity ratio in the cw spectra with decreasing Bl!. The dependence of r on the magnetic field is displayed in Fig. 3(b). A decrease of r with increasing B~ is observed. It is not possible to conclusively identify the relaxation time T with the M s reversal time T s for two reasons: It is not clear for the moment if the equilibrium between all radiative states is not rather determined by the low-energy localized states and it is also possible that the relaxation from B to A occurs through optically inactive intermediate states.

An effect of the magnetic field on the PL rise time can be found for low magnetic fields Bl~ ~< 8 T. In Fig. 4 the PL transients of exciton B under excitation of the light-hole level E: at Brl --- 0 and 8 T demon- strate a displacement of t 0, the time of maximum PL intensity, by roughly 100 ps towards shorter times. The same behaviour is observed for the A exciton under excitation of the light-hole level E~. Since the PL decay time is roughly the same for magnetic fields BrI~<8T, the shift of t o must be the result of a shortening of the rise-time. On the other hand, for higher fields (B, = 12 T) the displacement of to (not shown here) is a consequence of the decrease of the decay time r~.

Following Refs [2, 3] the slow rise-time at B, = 0T is always observed for laser excitation with excess energies of several meV above the heavy-hole exciton. The rise time reflects the slow exciton cooling through emission of acoustical phonons and it is decreased by reducing the excitation energy[3]. In our case, we kept the laser energy resonant with the light hole exciton that is 11 meV above the heavy-hole exciton. The effect of the magnetic field is to shift the (ej, hh~) continuum to higher energies than the K ~, 0 states of the light-hole exciton for Bj~ > 5 T and at B, = 8 T only K ~ 0 light-hole excitons are excited. The faster PL rise time that we observe is consistent with rise-times found in Ref. [3] under similar exciton densities (10~°cm -2) and for a larger QW sample where light-hole excitons could be excited selectively. In our case, the magnetic field allows to modify the energy spectrum and thus to shorten the PL rise time.

SUMMARY, CONCLUSION

In summary, the time-resolved magneto-optical experiments show that relaxation between the light and heavy-hole magnetoexcitons occur preferentially with conservation of the electron spin. As a consequence, under excitation conditions which favour the higher Zeeman split component, a highly non-thermal population of the i s heavy-hole excitons is created and can be observed during the first 100 ps after the excitation pulse. Increasing the magnetic field leads to a higher degree of spin conservation during the relaxation from the light to the heavy-hole excitons and also to a faster thermalization between the two Zeeman split components. The net result of

100

. d 1

0.1 -200

Excitons in a GaAs quantum well

_ A O21T

0 5 2 p s x~ ~ " ~ v v ~ o V v '~

0 ~ 0 0

o° \ " ~ " k ~ - ' - ' ~ - ~ ~ o ooo o \ ~ - - o o o o

I I~ I GI Qo_l 0 200 400 600 800

Time (ps)

140 D

- - 4.4

.-.. 120 -- 4.2

4.0 "-- 100 - -

3.8 %

.-~ 80 - _=

< 3.6

60 - 3.4

40 ~ I ] [ [ 3.2 10 12 14 16 18 20 22

B-field (T)

Fig. 3. (a) Temporal behaviour of the intensity ration B/A on a semi-log, scale showing an exponential decay with a lifetime ¢ ( = 52 ps at 21 T) for the relaxation of the exciton populations at different values of the magnetic field. Note the decrease of T but the increase of the amplitude I 0 with increasing magnetic field. The curves for 14 and 18 T are vertically shifted for clarity. (b) Dependence of the thermalization time r and of the excess population 1o/1 (t ---, oo) upon magnetic field. The dashed and solid lines are guides

to the eye.

927

1.2 x 105

~ 0.9 x 10 5 ~2

;~ 0.6 x 10 5

0.3 x 105

.1

0

. . . . 8T t~, ~ 0T

0 500 1000

Delay (ps)

Fig. 4. Normalized PL transients of exciton B under excitation of E 2 for 0 and 8 Tesla. The time of maximum PL intensity to is displaced by 100 ps to shorter times at 8 T

revealing a decrease of the PL rise-time.

these two effects explains the cw spectra and the first effect is in agreement with previous interpretations. The faster thermalization, hardly accessible with cw experiments, gives new insight into spin dynamics of magneto-excitons. Further experiments clarifying the role of the localized excitons are needed to identify the thermalization time within the I s heavy-hole exciton components with the magnetic moment reversal time.

In addition, in the range of lower magnetic fields a field-induced decrease of the PL rise-time is observed which can be related to the selective excitation of light-hole excitons for B N > 5 T in our particular sample. In order to clarify such an effect of the density of states modified by the magnetic field, the low field region should be studied more carefully.


Acknowledgements--We wo~lld like to thank H. Krath for technical assistance. S.H. is grateful for a scholarship from the Deutscher Akademischer Austauschdienst (HSPII/AUFE).

REFERENCES

1. M. Potemski, J. C. Maan, A. Fasolino, K. Ploog and G. Weimann, Phys. Rev. Lett. 63, 2409 (1989).

2. T. C. Damen, J. Shah, D. Y. Oberli, D. S. Chemla, J. E. Cunningham and J. M. Kuo, Phys. Rev. B 42, 7434 (1990).

3. R. Eccleston, R. Strobel, W. W. Rfihle. J. Kuhl, B. F. Feuerbacher and K. Ploog Phys. Rev. B 44, 1395 (1991).

4. B. Deveaud, F. Cl~rot, N. Roy, Satzke. B. Sermage and D. S. Katzer, Phys. Rev. Lett. 67, 2355 (1991).

5. T. C. Damen, L. Vifia, J. E. Cunningham. J. Shah and L. J. Sham, Phys. Rev. Lett. 67, 3432 (1991).

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High magnetic field effects on the dynamics of excitons in a GaAs quantum well