Journal of Luminescence 45 (1990) 181 185 NorthHolland
181
EXCITON DYNAMICS IN GaAs QUANTUM WELLS T.C. DAMEN, Jagdeep SHAH, D.Y. OBERLI, D.S. CHEMLA, J.E. CUNNINGHAM and J.M. KUO AT & T Be!! Laboratories, Holmdel, NJ 07733, USA
We show that excitons in GaAs quantum wells are formed in less than 20 ps following subpicosecond optical excitation. The rise of exciton luminescence is surprisingly slow ( = 400 ps) in spite of the fast formation of excitons. The slow rise of exciton luminescence shows unusual dependence on temperature, density and excitation energy. We show that the slow rise of exciton luminescence is caused by the slow relaxation of excitons within the excitonic branch. These studies raise a number of fundamental issues which are discussed.
Optical properties of excitons in quantum wells have been the subject of intense research in recent years [1,21. The dynamics of exciton ionization [3], the AC Stark effect of excitons induced by an intense optical field [4,5], the homogeneous linewidth of excitons, and the influence of temperature and various collisions on this linewidth [6], and the recombination dynamics of exci
tons have been investigated by ultrafast spectroscopy [7]. In spite of this intense interest in excitons, one important aspect of excitons, the dynamics of formation of bound states of excitons following photoexcitation of electron hole pairs, has remained totally unexplored, We present the first such results in this paper. The ionization of photoexcited (K 0) excitons occurs primarily by interaction with longitudinal optical (LO) photons and is well understood. However, the inverse process of exciton formation is considerably
Two highquality GaAs/AIGaAs multiple quantum well (MQW) samples were investigated; for sample A, the MQW was in the i region of a pin structure and had 50 periods, a well thickness of 50 A and Al concentration of 0.35 in the barriers. Sample B had 50 periods, a well width of 80 A. and an Al concentration of 0.3 in the barriers. Both samples gave nearly identical results, except that the helium temperature decay time for excitons was 500 ps for sample B and 300 Ps for sample A. All the data presented in this paper are for sample B unless indicated otherwise. The samples were mounted on a cold finger in a Helitran (temperature range 10 to 300 K) and were excited with a LD750 dye
laser, synchronously pumped with the second harmonic of a compressed, modelocked YAG laser. The laser was tunable between 720 and 800 nm and the pulsewidth was < 0.7 ps. Subpicosecond luminescence spec
more complex and not understood. Photoexcited dcctron and hole (either from a geminate or a nongeminate pair) can form an exciton by interaction with acoustic and optical photons, and also by carrier carrier interactions. The relaxation of photoexcited pairs within the bands proceeds simultaneously with the exciton formation process. Also, the excitons can be initially formed
troscopy was performed using the upconversion technique [8]. Most of the data were obtained at an excitation density of I X lO~~ cm 2 per well to avoid any complications arising from screening of excitons and bandgap renormalization effects. Figure 1 shows the time evolution of the luminescence at the exciton peak for various temperatures. T
in the ground as well as excited states, and in the singlet as well as triplet states (corresponding to the ortho and parahydrogen states). Furthermore, the excitons are very likely created with a large total momentum wave vector, K, corresponding to the centerofmass motion of exeitons in the quantum well planes. The relaxation of these nonthermal excitons into the singlet K — 0 state (the only state that can directly couple to the photons) must also be considered. This brief discussion makes it apparent that an investigation of the dynamics of exciton formation and relaxation has the potential of providing new insight into many facets of exciton physics that have not been considered before.
defined as the time required for the exciton luminescence to reach the maximum intensity, is nearly 300 Ps at 10 K and decreases dramatically with increase in the lattice temperature. The initial increase in the exciton luminescence intensity is the same at all temperatures. but the peak is reached much sooner, and the maximum intensity is much smaller at higher temperatures. r~ is <20 ps at 60 K. Figure 2 shows the time evolution of exciton luminescence for three different excitation densities. The density range of 2 x iO~to 5 x 1010 cm 2 per well was investigated in this study. With decreasing excitation density, Tf increases and then saturates at 400 ps
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Exciton dynarnic.s in GaAs quantum wel!s
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200 400 DELAY (ps) Fig. 3. The time evolution of exciton luminescence at the spectral peak (1.568 eV) of sample A for three different excitation photon energies. The high energy tails and the broadening disappear
for excitation density < 5 x iO’ cm 2 per well. We have investigated the dependence of r 1 on the excitation photon energy in the range 17 meV to 100 meV above the exciton energy and specifically investigated the cxcitation at the light hole exciton energy and also at one LO phonon above the exciton energy. The data show that, within the experimental uncertainty, the time
with increasing time delays. The luminescence spectrum
evolution of exciton luminescence is independent of the excitation energy in this range. Representative time evolution curves for sample A, with larger separation
spectra at short times represents a significant broad ening of the exciton luminescence compared with the cw spectral width. There was no measurable shift in the
between the heavy and the light hole excitons, are
peak energy of the exciton luminescence as a function of time, showing that we are investigating intrinsic exciton properties. We begin the analysis of the data by recalling that only those excitons within the homogeneous linewidth (~)of K 0 can directly couple to radiation [9]. We
shown in fig. 3.
Typical timeresolved luminescence spectra at two time delays are shown in fig. 4(a). At short delays, the spectra are broad and have distinct high energy tails,
at long (> 1 ns) time delays has a full width at half maximum (FWHM) of 7 meV, which corresponds to a convolution of the cw spectral width (= 3 meV, caused
by inhomogeneous broadening), the spectrometer resolution (2 meV) and the spectral width of the short pulse laser. The observed FWHM in the time resolved
visualize that the relaxation of photoexcited electron I
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T. c. Damen et a!. / Exciton dynamics in GaAs quantum we!ls
hole pairs into K = 0 excitons may be affected by three processes: (1) initial thermalization and the subsequent cooling of the photoexcited pairs, (2) emission of acoustic or optical phonons by an electron hole pair leading to the formation of excitons, preferentially at large K vectors, and (3) relaxation of the large K excitons into the K— 0 excitons [10,11]. To investigate which process dominates, we determine the relative density of electron hole pairs and excitons as a function of time by analysing the spectral
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shape of the luminescence, which is a superposition of the K — 0 exciton luminescence and the electron hole
pair luminescence. The emission from the excited states (n> 1) of the exciton is negligible compared to that from the ground state because the oscillator strength decreases as (n — ~) ~.In the spectra in fig. 4(a), the spectral peak corresponds to the exciton luminescence, while the high energy tail corresponds to the bandtoband luminescence. We find that, even at the shortest time delays (< 1 ps), the excitonic luminescence
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dominates the free carrier luminescence. However, this does not imply that the density of excitons is higher than the density of electron hole pairs, because the ratio of intensities depends not only on the densities and the relative oscillator strengths (or absorption coefficients) but also on the distribution functions of the electron hole pairs and the excitons. Since the distribution functions
Fig. 6. Integrated electron hole and exciton luminescence intensities as a function of time, obtained by curve fitting experimental spectra.
are not known, the observed intensity ratios cannot be used to determine the ratio of densities accurately. We determine the electron hole pair density by measuring the temporal evolution of the homogeneous linewidth of excitons, which is strongly influenced by the presence of electron hole pair density [6,12]. We consider that the exciton lineshape is a convolution of the Gaussian lineshape observed at long times (FWHM 7
Lorentzian within ±0.5 meV. The electron hole luminescence spectrum is then determined by subtracting this exciton lineshape from the measured spectrum. This procedure is illustrated in fig. 4(b) for the spectrum at 6.7 ps. The FWHM of the Lorentzian determined in this manner (fig. 5) shows a rapid initial reduction followed by a more gradual decrease. Since exciton electron collisions [13] are about an order of magnitude
meV) with a Lorentzian whose width is adjusted to give a good fit to the low energy side of the spectrum. This piocedure allows us to determine the width of the
more efficient in broadening excitons than exciton exciton collisions [6], the rapid initial reduction is at
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tributed to the decay of electron hole pairs into cxcitons and the more gradual decrease at later times to relaxation and decay of excitons. This analysis shows that the density of electron hole pairs decreases with a time constant of less than 20 ps, considerably shorter than the measured T by the rapid decay of the integrated hole pair 1. This conclusionelectron is also supported
luminescence intensity (fig. 6) and the cooling of the electron hole temperature with time determined from
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Fig. 5. The time dependence of FWHM of the Lorentzian from curve fitting described in fig. 4.
the high energy tail of electron hole luminescence. We. therefore, conclude that the electron hole pairs form large K excitons in less than 20 ps and that the primary cause of the long risetime of exciton luminescence is the slow relaxation of large K excitons to K 0 excitons. The data presented in figs. I and 2 strongly support
this conclusion. To understand the temperature dependence, we note that the measured intensity is proportional to R, the rate of radiative recombination of — n ~/Tr, n~ 0 is the density of cxci
excitons, where R
184
1(1 Damen eta!.
Exciton d3namics in GaA3 quantum wells
tons within zl of K 0 and ~ is the exciton radiative recombination lifetime, determined by the exciton osctllator strength. At low temperatures (10 K), the thermalized exciton distribution is sharply peaked near K 0, and it takes a long time for the initial distribution of large K excitons to relax towards the thermalized distribution. This explains the long rise for the exciton luminescence at 10 K. Since n,, 0 is large for a sharply peaked distribution near K 0, the maximum lumines cence intensity is large. On the other hand, at higher temperatures (e.g. 60 K) the thermalized exciton distribution is spread out and the initial distribution of large K excitons approaches this distribution quite rapidly. At such temperatures, ionization of excitons by acoustic phonon absorption also contributes to the dynamics. In this case the rise of luminescence is rapid and may in fact be limited by the capture of electron hole pairs into excitons. Also, n,,0 is relative small because only a small fraction of all excitons are near K 0: therefore, the peak luminescence intensity is considerably smaller than for 10 K. The data at intermediate temperatures can be qualitatively explained by similar arguments. The relaxation of large K excitons to those that can radiate takes place via exciton exciton collisions and exciton acoustic phonon collisions. The decrease of Tf with increasing density (fig. 2) for a density greater than 4X cm 2 per well shows that exciton exciton collisions dominate above this density and exciton acoustic photon collisions dominate below this density. Assuming collisions between hard disks, the exciton exciton collision time is inversely proportional to the exciton density and velocity (and hence ~ At the above density and T 10 K, this time is estimated to be 30 PS. We conclude that the effective exciton acoustic photon collision time for exciton relaxation is about 30 p5. While exciton acoustic photon interactions relevant to exciton linewidth have been investigated [15 17], re
laxation of excituns within the exciton branch remains to be explored, and no comparison with calculations is possible at this time. It is also interesting to note that in
the absence of exciton exciton collisions, the exciton distribution remains non thermal and continues to relax towards the lowest energy exciton state until all excitons recombine. Also, the observed density dependence implies a nonthermal distribution of excitons. The observation (fig. 3), that the formation time is independent of the initial excess energy of the photoexcited electron hole pairs, strongly supports the earlier conclusion that the relaxation within the exciton branch is the primary cause of the slow rise of the exciton luminescence. It also supports the idea that the exciton distribution is nonthermal. Perhaps a more fascinating aspect of the data is that no resonance is observed when the photon energy coincides with the light hole exciton or when the photon energy is exactly one LO phonon energy larger than the exciton. Since an electron hole
pair can emit a phonon in about 100 fs, why is the formation time not shortened? We believe that one possible answer is that since the homogeneous linewidth is considerably (by about a factor of 20) smaller than the inhornogeneous linewidth, the direct creation of K 0 excitons occurs in only a small area of the quanturn wells. This will considerably dilute the effect of the
resonance. While this appears to be a plausible explanation, a definitive interpretation must await further investigations. In conclusion, we have presented the first investigation of the dynamics of the exciton formation and relaxation in a semiconductor. We have shown that electron hole pairs disappear quickly (< 20 ps) but that relaxation within the exciton branch to the K 0 cxciton can take several hundred picoseconds, leading to a long rise time for the exciton luminescence. A number of fundamental questions concerning excitons in quan
turn wells have been addressed, and a good qualitative picture for the formation and relaxation of excitons has been developed.
References [1] S. Schmitt Rink, D.S. Chemla and DAB. Miller, Advan. Phys. 38 11989) 1. 121 DAB. Miller, D.S. Chemla, T.C. Damen, T.H. Wood, CA. Burrus, AC. Gossard and W.W. Wiegmann, IEEE J. Quant. Electron. QE21 (1985) 1462. [31 W.H. Knox, R.L. Fork, MC. Downer, DAB. Miller, D.S. Chemla, C V. Shank, A C. Gossard and W. Wiegmann, Phys. Rev. Lett. 54 (1985) 1306. [~l A. Mysyrowicz, D. Hulin, A. Antonetti, A. Migus, W.T Masselink and H. Morkoc, Phys. Rev. Lett. 56 (1986) 2748; A. von Lehman, D.S. Chemla, J.E. Zucker and J.P. Ilentage, Opt. Lett. 11(1986) 609. [5] W H Knox, fl,S (‘hernIa, 1) A H Miller, I B Stark and S SchmittRink, Phys. Rev. Lett. 62 (1989) 1189. [61 A. Honold, Schultheis, J. KuhI, andeds. C.W. in Proc. Ultrafast VI,L.Mt Hiei, Japan (1988). T Tu, Yajima. K.
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[71 L
Feldmann, G Peter, E.O. Göhel, P Dawson, K. Moore,
C. Foxori and R.J. Elliott, Phys. Rev. Lett. 59 (1987) 2337 [8] J. Shah, IEEE J. Quant. Electron. QE 24 (1988) 276. [91 The incident exciting photon is perpendicular and the emitted photon is nearly perpendicular to the quantum well plane. Therefore, the electron hole pairs are created with the total inplane momentum K 0 and only K 0 excitons emit light [101 plane, For a the photon propagating normal to the quantum pair well relative wavevector k of the photoexcited is the same as k,, and will have an uncertainty related to the spectral width of the excitation pulse. From the uncertainty principle, we estimate that the spatial extent of the electron hole wavepacket varies from about 200 A to 600 A for the excitation energies used in our experiment. If
I c. Damen et a!. / Exciton dynamics in GaAs quantum wells
185
there are frequent longrange Coulomb collisions, then the
[12] R.C.C. Leite, J. Shah and J.P. Gordon, Phys. Rev. Lett. 23
excitons will be created from the geminate pair and there will be no triplet excitons. For less frequent collisions, the
[13] Note that holes are less effective in broadening exciton
rapidly moving electron will go away from its geminate hole, the exciton can be formed from nongeminate pairs, and triplet states may play an important role. [11] An electron hole pair can form an exciton without losing any energy: however, such an exciton can autoionize just as easily. We therefore consider only those excitons whose kinetic energy is less than the exciton binding energy.
(1969) 1332. since F is inversely proportional to the carrier mass. [141 T. Takagahara, Phys. Rev. B32 (1985) 7013. [15] Johnson Lee, E.S. Koteles and M.O. Vassel, Phys. Rev. B33 (1985) 5512. [161 S. Rudin, and T.L. Reincke, Superlatt. Microstruct. 3 (1987) 137.