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ZnTe quantum wells
JOURNALOF
LUMINESCENCE Journal of Luminescence 58 11994) 216
ELSEVIER
222
Invited paper
Exciton dynamics in zinc-rich CdZnTe/ZnTe quantum wells J.F. Donegan*, R.P. Stanley, J.P. Doran, J. Hegarty Optronzc~Ireland Research Centre, Department of Pure and Applied Physics. Tnnitv College. Dublin 2. Ireland
Abstract
In this review we detail the dynamics of intrinsic excitons in the alloy Cd~Zn1~TeZnTe quantum well system. We measure the spectral d~ffusionof excitons within the inhomogeneously broadened line by time-resolved luminescence. We observe non-resonantfluorescence line narrowing in these materials which leads to sharp lines sitting on top of the broad exciton luminescence. Using both lifetime and dephasing measurements these lines are found to be predominantly luminescent in nature. The thermal broadening of the exciton due to longitudinal optical-(LO-) phonon scattering is measured up to room temperature and is found to be well-width dependent. The extent of the exciton localisation in this material can be deduced by a comparison of the dephasing and spectral diffusion times with other systems. 1. Introduction Excitons in II VI materials have a strong interaction with photons and phonons. The exciton photon interaction gives rise to strong excitonic transitions. In quantum well structures excitonic transitions are enhanced over bulk materials because of confinement effects. The absorption and luminescence properties of the lowest energy heavy-hole excitons can be used as an effective tool in the study of interfacial and alloy roughness and of general materials quality, The strong exciton phonon interaction in II VI materials leads to thermal broadening of the excitonic transitions, [1] to hot exciton effects [2] and to phonon replicas in the optical transitions [3]. Thermal broadening is an important factor in determining the potential for room-temperature quantum well excitonic devices. The creation of hot excitons has been a source of controversy as it can *
Corresponding author.
be difficult to distinguish it from resonant Raman scattering [4]. The existence of disorder due to alloy and interface roughness has been shown to strongly affect the localisation and dephasing properties of excitons. In III V quantum wells interface roughness can lead to localisation of excitons while in bulk II VI materials alloy disorder leads to strong localisation. In this paper, we present a study of exciton dynamics in wide-gap Cd~Zn1 ~Te/ZnTe quantum wells. In particular we consider spectral diffusion, non-resonant fluorescence line narrowing, luminescence decay times, dephasing and thermal broadening due to scattering of phonons.
2. Sample details The samples used in this study were grown by molecular beam epitaxy on GaAs substrates. A 2 j.tm thick ZnTe buffer layer was used to produce
0022-2313 94 807.00 C 1994 Elsevier Science By. All rights reserved SSDIOO22-2313(93)E0l45-N
J.F. Donegan et al. Journal of Luminescence 58 (1994) 216 222
217
Table 1 Samples of Cd~Zn~je/Zn Te used in our studies Sample
Buffer
Si
2pm ZnTe
S2 S3 S4 S5 S6 S7 S8
2pm ZnTe 2pm ZnTe 2pm ZnTe 1pm Cd 14Zn 86Te 2pm ZnTe 2pmZnTe 2pm ZnTe
Barrier
Well
soA Cd iooA Cd
50A ZnTe
13Zn 8~Te 13Zn 87Te 3OACd25Zn15Te 5OACd25Zn75Te 50A Cd 25Zn 5Te 40A Cd 33Zn 67Te 7OACd33Zn67Te 100ACd33Zn67Te
iooA ZnTe 100AZnTe 100AZnTe iooA ZnTe 140A ZnTe I4OAZnTe 14OAZnTe
a strain-free surface on which the quantum wells were grown. Both single and multiple quantum well (SQW and MQW, respectively) structures were grown with Cd~Zn1 ~Te wells and ZnTe barriers. Cd concentrations in the wells range from 13% to 33% with well widths from 30 to 100 A. Details of specific samples will be given as they occur and are summarized in Table 1.
3. Luminescence decay and spectral diffusion A good indication of the II VI quantum well material quality is the low-temperature exciton line width observed in absorption and photoluminescence (PL). Fig. 1(a) shows the luminescence spectrum for the 40 A single quantum well sample S6. The heavy-hole exciton has a half-width at halfmaximum (HWHM) of 4.1 meV. In all the samples studied, the widest heavy-hole exciton line width is only 5 meV. There is no strong correlation between well width and line width in all the samples in Table 1, so alloy broadening seems to make the dominant contribution to the low-temperature exciton line width. The smaller exciton diameter in the quantum well results in a larger exciton line width than in bulk materials of the same composition. Fig. 1(b) shows the photoluminescence excitation (PLE) spectrum obtained by monitoring the low-energy edge of the exciton luminescence. We observe that the exciton profile is produced in the PLE spectrum but is shifted slightly to higher energy. Also shown in Fig. 1(c) is the variation of the luminescence decay rate across the exciton line,
Periods x x x x x
15 10 10 10 10 x 1 xl xl
I
:
S6 40 A .
Cd0•33Zn0~67Te
(b) .~
(c) .....-
(a)
. ..~.
~...
214216218220
Energy (eV) Fig. 1. Photoluminescence (a) excitation spectrum (b) and luminescence decay time (c) for the 40 A Cd0 33Zn0 6~Te/ZnTe single quantum well (S6) taken at 10 K.
These results suggest that spectral diffusion of the excitons is occurring within the exciton profile. The absorption of light leads to the formation of excitons in regions of varying potential due to the alloy nature of the well material. Excitons created on the high-energy side of the exciton line can recombine radiatively where they were created or they can move to a different environment and therefore to a new spectral position within the exciton line where they can in turn either recombine or diffuse. The process of exciton movement within the exciton profile is called spectral diffusion. At the low temperatures of our experiments, the relaxation within the exciton line occurs through acoustic phonon assisted hopping [3] and
218
J.F. Donegan et al.
Journal oJ Luminescence 58 (1994) 216 222
will be predominantly to lower energy. The process of relaxation means that under steady-state conditions, states low in the exciton line will become more heavily populated than those higher up and so the peak position of the exciton line in luminescence is shifted from the peak in absorption. This shift in energy (1.0meV) has become known as the Stokes shift and it is a measure of the spectral diffusion within the exciton line. In Fig. 2 we present time-resolved luminescence spectra for the same SQW sample (S6). These spectra allow us to see the exciton profile as it evolves in time and thus to observe directly the process of spectral diffusion within the exciton line, In this figure the peak of the exciton at short times is indicated by a vertical line at 2.18 1 eV as a guide to the observation of spectral diffusion. After a time of 200 ps we observe that the exciton peak has shifted by about 1 meV to lower energy and that
S6:
40
X 1
X 1 8
For excitation energies far above the band gap, the exciton luminescence line shape is independent of pump position. In Fig. 3 we show two very
A
~ 97 Ps
4. Non-resonant fluorescence line narrowing At low temperatures, all samples show strong intrinsic excitonic luminescence. The width of the exciton luminescence line is similar to its width in absorption and ranges from 4 to 5 meV (HWHM). However, we find that in these samples the shape of the exciton luminescence line also depends on the wavelength position of the excitation source.
Cd33Zn,~7Te
0 ps
after this time no further shift of the line occurs. The Stokes shift of I meV is very similar to that observed in the steady-state spectra in Fig. 1. These time-resolved spectra show that spectral diffusion occurs within a time of 200 ps. The increase in the exciton decay rate from low- to high-energy side in the exciton profile is a result of the spectral diffusion process. As the excitons migrate to lower energy, further spectral relaxation becomes more difficult as the excitons become increasingly more localised by the alloy potential fluctuations. We note that the exciton recombination and spectral diffusion times are comparable and they indicate an overall slow rate of spectral relaxation within the exciton profile in Cd~Zn1 ~Te/ZnTe.
1~x86 S3 30 A Cd
i~—
A LO
Zn ~ Te wells
~
~“
_________
2.170
1
•~~_,_
2.175 Energy(eV)
2.190
Fig. 2. Time-resolved photoluminescence spectra for the 40 A Cd0,3 3Zn0 67Te/ZnTe single quantum well (S6) under 20 ps excitation. The spectra at different times are normalised showing the small change in line shape with time. The multiplication factor is shown on the right. The vertical line at 2.181 eV is a guide to the eye to show the gradual shift of the luminescence peak with increasing time,
°-
~
‘
LO”
2240
2 256
Energy (eV)
Fig. 3. Luminescence spectra for sample S3 30 A Cd0 25 Zn0 75Te ZnTe MQW structure with different pump energies; 2.268 (continuous line) and 2.28 1 eV (dashed line). Note the sharp lines labelled L01, LO, LO”, L02.
J.F. Donegan el a!.
different PL spectra for the
Journal of Luminescence 58 (1994) 216 222
30A Cd0 25Zn0 75Te/
ZnTe MQW sample (S3). The spectrum shown as a dashed line is similar to the normal exciton line shape. Compare this to the second PL spectrum shown in Fig. 3 as a solid line. Here the PL was excited using a narrow band laser just 20meV above the centre of the exciton line. At the middle of the exciton line, a prominent sharp line appears on top of the background luminescence. As the exciting laser is tuned, two sharp lines labelled LO (also seen weakly in the dashed-line spectrum) and L02 move across the exciton luminescence. The energy separation between these lines and the excitation laser stays constant regardless of the excitation energy and both lines only appear superimposed on the background exciton luminescence, The L01 line is shifted from the laser line by 25.6meV which we associate with the ZnTe-like LO phonon while line L02 is shifted 20.3 meV and is associated with the CdTe-like LO phonon in Cd~Zn1 ~Te. Although these assignments are the same as for resonant Raman scattering [5], we will show that the sharp lines are predominantly luminescent in nature at low temperature. The luminescence spectra of Fig. 3 show that excitons in different parts of the inhomogeneously broadened exciton luminescence behave differently and can be selectively probed. By monitoring a narrow spectral region in emission as in a luminescence excitation experiment, the creation and relaxation channels for a subset of excitons can be investigated. This is a form of fluorescence line narrowing (FLN). FLN normally occurs when an inhomogeneously broadened line is excited resonantly by a narrow band laser. Provided that there is little spectral relaxation across the line, the fluorescence originates only from the subset of states excited and is narrower than the full inhomogeneous line width. Our data on Cd~Zni ~Te/ZnTe quantum wells represent a different type of FLN in which the excitation is non-resonant with the emission. The process that forms the sharp lines is explained as follows: Consider narrow band pumping at an excitation energy. Ee~c E0 + nELO, where ELn is the LO-phonon energy, E0 is the exciton ground state energy in just one part of the inhomogeneous line and n is the phonon number (n 1 for the case in =
=
219
Fig. 3). The excitons created by the pumping have large momenta and are called ‘hot’ excitons. Hot excitons preferentially relax by LO-phonon emission to the ground state at k 0. This can create a narrow distribution of excitons because the energy of the participating LO phonons is well defined. Given a low rate of spectral diffusion, as discussed earlier, the excitons will remain in a narrow band for long enough to radiatively recombine, giving rise to a sharp line. There will also be a background luminescence signal because free carriers will also be created which relax non-preferentially into the exciton line. Hence we expect to see two sharp lines involving the L01 and L02 phonons. respectively, superimposed on a broader background luminescence (Fig. 3). In our quantum well materials the intrinsic luminescence is dominated by excitonic recombination. It is to be noted that lasing action has been observed in these materials at efficiencies equivalent to those found in high quality III V materials [6]. In addition, the spectral diffusion rate is low, as indicated by the small Stokes shift between excitation and emission (Fig. 1(a)). This allows the formation of sharp lines as detailed previously both with high radiative efficiencies and long lifetimes. As the sharp line modes are LO-phonon replicas, we must consider the possibility that they are due to resonant Raman scattering. There has always been some controversy over the distinction between resonant Raman scattering (RRS) and luminescence [4]. Raman scattering is a direct process involving virtual states, while luminescence is absorption into real states followed by emission. However, near-resonance real states can be involved in the scattering process and when phonon replicas are observed experimentally, their origin as luminescence or resonant Raman features may be ambiguous. Theory [7] indicates that a more correct view is to consider the phase (or transverse) relaxation time T2 and the energy (or longitudinal) relaxation time T1 for the material under study in so far as they can be defined. Resonant Raman scattering is considered to occur over a time T2 while luminescence occurs over a time T~. In the case that T2 is determined by T1, the distinction between the resonant Raman and luminescence processes becomes meaningless. T~ and T2 —
220
J.F. Donegan et al.
Journal of Luminescence 58 (1994) 216 222
can be measured in time-resolved experiments. At resonance, the ratio of the resonant Raman scattering to the luminescence is proportional to the ratio of the phase to the energy relaxation time such that I(Raman) I(Luminescence)
I
S6.40A —12.7meV
(1)
.E
For an exciton in a semiconductor, loss of coherence may arise from scattering with free carriers, other excitons, acoustic and optical phonons, lattice imperfections and other fluctuations in the crystal field. In our Cd~Zni ~Te/ZnTe quantum well structures, we have measured the lifetime of the excitons by time-resolved photoluminescence and their coherence decay time by time-resolved fourwave mixing. The results of these experiments show that the decay time of the sharp lines (115 ps) is similar to the decay of the underlying luminescence (120 ps) and that this decay time is much longer than the coherence time of the excitons (25 p5 measured by four-wave mixing on the low-energy side of the exciton absorption). Under the criterion that T2 << T1, we conclude that the sharp lines are predominantly luminescent in nature and are not due to resonant Raman scattering. Knowing the dephasing time is important if the problem of resonant Raman scattering versus luminescence is to be avoided and also because it is difficult to make assumptions on the values of dephasing times. Dephasing times can have a large range depending on the material.
~
cC
.
T
10 K
ph 70 K
1 150K
~ ~
290 K .
I
I
2.05
2.10
_______________________
2.15 Energy (eV)
2.20
Fig. 4 Photoluminescence spectra as a function of temperature for the 40 A Cd 33Zn57Te/ZnTe single quantum well sample (S6) showing the dominance offree exciton recombination upto room temperature.
high-energy tail due to free-carrier recombination. The SQW samples have the narrowest low-temperature line widths of our Cd~Zn1 ~Te/ZnTe samples as well as the weakest defect luminescence. These are the most recently grown samples and indicate that II VI materials are rapidly catching up on their III V counterparts in material quality. The main interaction that determines the thermal broadening is believed to be the scattering of excitons from K 0 states by LO phonons. This interaction homogeneously broadens the line with the homogeneous line width given by [9] /
(2)
-\
i E~0~
5. Thermal broadening of the exciton line by LO phonons As the temperature increases, the exciton absorption and PL lines broaden out. The extent of the thermal broadening varies with well material and also with well width [8]. In Fig. 4, we show the luminescence spectrum of the single quantum well (SQW) sample S6 as a function of temperature. This spectrum, as with all the SQW samples, is dominated by free exciton luminescence even up to room temperature. Note that the exciton line has broadened with increasing temperature and the exciton line at room temperature has a pronounced
explkT,
1
\
This is just the phonon interaction factor, [‘ph’ multiplied by the phonon occupation number, where EL0 is the LO-phonon energy and kT is the thermal energy. For all our samples the low-ternperature exciton line shapes are almost exactly Gaussian. The observed exciton line widths are a convolution of a Gaussian profile due to inhomogeneous broadening with the Lorentzian profile of the homogeneous line width. The resulting measured line shape has a Voigt profile and as it has no analytic expression, a numerical deconvolution procedure is required to determine the homogeneous line width. The fit to the HWHM widths
J.F. Donegan et a!.
gives
[‘ph
energy
/ Journal of Luminescence
as 12.7 meV using the ZnTe LO-phonon
ELO 26.1 meV. This compares to 5.5 meV in GaAs [10] and to ~‘ph 10.5 meV in In~Ga1 ~As quantum wells [11]. The thermal broadening depends on several factors. The smaller LO-phonon energy in these materials leads to higher phonon occupancy at room temperature than in either GaAs or In~Ga1 LAs. The phonon interaction factor [‘ph has two contributions: the Fröhlich parameter and an integral over possible scattering states. The Fröhlich parameter, ~ is a material parameter which decreases on going from pure ZnTe to pure CdTe and describes the strength of the LO-phonon electron interaction. The integral over scattering states depends non-linearly on the number of final states into which the excitons and the resulting electron hole pairs can scatter. In general, this decreases with increasing exciton binding energy. It should also decrease with decreasing well width as fewer electron and hole subbands become available within an LO-phonon energy of the exciton, on going to narrower wells. For the SQW samples we find [‘ph varies from 12.7meV for the 40A samples 17.0meV for the 70A sample to 19.0meV for the 100 A sample. Of the samples studied we find that the SQW sample with a 40A well and 33% Cd concentration has the smallest resulting [‘ph. From [8] we find that [‘ph can be reduced considerably if the exciton binding energy can exceed the LOphonon energy, a situation unique to II VI materials. This has led to the proposal of new optoelectronic II VI devices such as the room-temperature exciton laser, [‘ph
=
—
=
6. Exciton localisation The alloy nature of the CdZnTe material results in the formation of excitons in regions of potential fluctuations. Comparing the dephasing and spectral diffusion times with other materials allows us to form an impression of the extent of exciton localisation in our materials. At Helium temperatures. delocalised excitons lose phase rapidly through elastic scattering of impurities and interfaces as observed in GaAs SQWs (T2 2ps [11]) and through elastic scattering from alloy fluctu-
ations
58 (1994) 216 222
as
observed
221
in
In~Ga1 ~AsMQWs
(T2 0.5 Ps [12]). For localised excitons dephasing is usually associated with inelastic scattering and may be orders of magnitude slower. In In~Ga1 5As MQWs [13] acoustic phonon assisted tunnelling leading to spectral diffusion results in T2 3Ops, while in CdS5Se1 dephasing is almost lifetime limited with T2 times as long as 400ps [14]. These results indicate that for strongly localised excitons the spectral diffusion time is long and the dephasing time is determined by the diffusion time. For delocalised excitons, on the other hand, the dephasing time is very short, on the order of 1 ps. The observed dephasing time of 25ps in our samples indicates that the excitons are not delocalised and this is supported by the slow spectral diffusion rate. The fact that T2 is considerably less than the diffusion time indicates that our excitons are not completely localised. The excitons have a characteristic localisation length which is large enough to allow some dephasing by elastic scattering but small enough to prevent rapid spectral diffusion. ~,
7. Conclusion In this paper we have measured the optical properties of the lowest energy heavy-hole exciton in Cd~Zn1 5Te/ZnTe quantum well structures. We have measured the extent of spectral diffusion of excitons within the inhomogeneously broadened line by time-resolved luminescence. While there is some diffusion, it is weak and the excitons are localised at low temperature. This is borne out by the fact that there is very little shift of the luminescence peak from the absorption under steady-state conditions. We have also observed non-resonant fluorescence line narrowing in these materials in which the direct creation of hot excitons can lead to sharp lines sitting on top of the inhomogeneously broadened exciton line at low temperature. By a combination of picosecond time-resolved luminescence and four-wave mixing, we have measured T1 and T2 for the excitons and have identified the sharp lines as due to luminescence rather than resonant Raman scattering. The mechanism and strength of the thermal broadening of the exciton
222
iF. Donegan et al.
Journal of Luminescence 58 (1994) 216 222
has been measured up to room temperature. The extent of the exciton localisation can be deduced by a comparison of the dephasing and spectral diffusion times with other systems.
Acknowledgements It is a pleasure to acknowledge the contribution of the following people to our study: Dr. R.D. Feldman and Dr. R.F. Austin for growing these magnificent materials, Professor E.O. Göbel and Professor M.D. Sturge for helpful discussions, Dr. MO. Henry for the loan of cryogenic equipment, Dr. R. Fischer, Dr. J. Feldmann, and R. Hahn of the University of Marburg for help with the time-resolved luminescence experiments. References [1] R.P. Stanley, J. Hegarty, RD. Feldman and R.F. Austin, AppI. Phys. Lett. 53 (1988) 1417. [2] S. Permogorov, Phys. Stat. Sol. (b) 68 (1975) 9. [3] E. Cohen and M.D. Sturge, Phys. Rev. B 25 (1982) 3832.
[4] The arguments for and against this distinction are well summarised in the comment “Resonant Scattering or absorption followed by emission”, YR. Shen, Phys. Rev. B 14 (1976) 1772 and the reply by JR. Solin and H. Merkelo, Phys. Rev. B 14 (1976) 1775. [5] D.J. Olego, P.M. Racaah and J.P. Faurie, Phys. Rev. B 33 (1986) 3819. [6] AM. Glass, K. Tai, RB. Bylmsa, RD. Feldman, D.H. Olson and R.F. Austin, AppI. Phys. Lett. 53 (1988) 834. [7] Y. Toyozawa, J. Phys. Soc. Japan 41(1976) 400. [8] J.P. Doran, R.P. Stanley, J.F. Donegan, J. Hegarty, R. Fischer, E.O. Göbel, RD. Feldman and R.F. Austin, B 185and (1993) 566. Williams, Semiconductor and [9] Physica H.B. Bebbs E.H. Semimetals, ed. R.K. Williardson and AC. Beer (Academic Press, New York, 1972) p. 256. [10] DAB. Miller, D.S. Chemla, D.J. Eilenberger, P.W. Smith, AC. Gossard and W.T. Tsang, AppI. Phys. Lett. 41(1982) 679. [11] J.S. Weiner, D.S. Chemla, DAB. Miller, T.H. Wood, D. Silvo and Y. Cho, AppI. Phys. Lett. 46 (1985) 619. [12] L. Schultheis, A. Honold, J. KuhI, K. Kdhler and C.W. To, Phys. Rev. B 34 (1986) 9027. [13] M. Wegener, D.S. Chemla, S. Schmitt-Rink and W. Schafer, Phys. Rev. A 42 (1990) 5675. [14] J. Hegarty, K. Tai and W.T. Tsang, Phys. Rev. B 38 (1988) 7843. 1151 G. Noll, U. Siegner, E.O. Gbbel and S. Shevel, Phys. Rev. Lett. 64 (1990) 792.
LUMINESCENCE Journal of Luminescence 58 11994) 216
ELSEVIER
222
Invited paper
Exciton dynamics in zinc-rich CdZnTe/ZnTe quantum wells J.F. Donegan*, R.P. Stanley, J.P. Doran, J. Hegarty Optronzc~Ireland Research Centre, Department of Pure and Applied Physics. Tnnitv College. Dublin 2. Ireland
Abstract
In this review we detail the dynamics of intrinsic excitons in the alloy Cd~Zn1~TeZnTe quantum well system. We measure the spectral d~ffusionof excitons within the inhomogeneously broadened line by time-resolved luminescence. We observe non-resonantfluorescence line narrowing in these materials which leads to sharp lines sitting on top of the broad exciton luminescence. Using both lifetime and dephasing measurements these lines are found to be predominantly luminescent in nature. The thermal broadening of the exciton due to longitudinal optical-(LO-) phonon scattering is measured up to room temperature and is found to be well-width dependent. The extent of the exciton localisation in this material can be deduced by a comparison of the dephasing and spectral diffusion times with other systems. 1. Introduction Excitons in II VI materials have a strong interaction with photons and phonons. The exciton photon interaction gives rise to strong excitonic transitions. In quantum well structures excitonic transitions are enhanced over bulk materials because of confinement effects. The absorption and luminescence properties of the lowest energy heavy-hole excitons can be used as an effective tool in the study of interfacial and alloy roughness and of general materials quality, The strong exciton phonon interaction in II VI materials leads to thermal broadening of the excitonic transitions, [1] to hot exciton effects [2] and to phonon replicas in the optical transitions [3]. Thermal broadening is an important factor in determining the potential for room-temperature quantum well excitonic devices. The creation of hot excitons has been a source of controversy as it can *
Corresponding author.
be difficult to distinguish it from resonant Raman scattering [4]. The existence of disorder due to alloy and interface roughness has been shown to strongly affect the localisation and dephasing properties of excitons. In III V quantum wells interface roughness can lead to localisation of excitons while in bulk II VI materials alloy disorder leads to strong localisation. In this paper, we present a study of exciton dynamics in wide-gap Cd~Zn1 ~Te/ZnTe quantum wells. In particular we consider spectral diffusion, non-resonant fluorescence line narrowing, luminescence decay times, dephasing and thermal broadening due to scattering of phonons.
2. Sample details The samples used in this study were grown by molecular beam epitaxy on GaAs substrates. A 2 j.tm thick ZnTe buffer layer was used to produce
0022-2313 94 807.00 C 1994 Elsevier Science By. All rights reserved SSDIOO22-2313(93)E0l45-N
J.F. Donegan et al. Journal of Luminescence 58 (1994) 216 222
217
Table 1 Samples of Cd~Zn~je/Zn Te used in our studies Sample
Buffer
Si
2pm ZnTe
S2 S3 S4 S5 S6 S7 S8
2pm ZnTe 2pm ZnTe 2pm ZnTe 1pm Cd 14Zn 86Te 2pm ZnTe 2pmZnTe 2pm ZnTe
Barrier
Well
soA Cd iooA Cd
50A ZnTe
13Zn 8~Te 13Zn 87Te 3OACd25Zn15Te 5OACd25Zn75Te 50A Cd 25Zn 5Te 40A Cd 33Zn 67Te 7OACd33Zn67Te 100ACd33Zn67Te
iooA ZnTe 100AZnTe 100AZnTe iooA ZnTe 140A ZnTe I4OAZnTe 14OAZnTe
a strain-free surface on which the quantum wells were grown. Both single and multiple quantum well (SQW and MQW, respectively) structures were grown with Cd~Zn1 ~Te wells and ZnTe barriers. Cd concentrations in the wells range from 13% to 33% with well widths from 30 to 100 A. Details of specific samples will be given as they occur and are summarized in Table 1.
3. Luminescence decay and spectral diffusion A good indication of the II VI quantum well material quality is the low-temperature exciton line width observed in absorption and photoluminescence (PL). Fig. 1(a) shows the luminescence spectrum for the 40 A single quantum well sample S6. The heavy-hole exciton has a half-width at halfmaximum (HWHM) of 4.1 meV. In all the samples studied, the widest heavy-hole exciton line width is only 5 meV. There is no strong correlation between well width and line width in all the samples in Table 1, so alloy broadening seems to make the dominant contribution to the low-temperature exciton line width. The smaller exciton diameter in the quantum well results in a larger exciton line width than in bulk materials of the same composition. Fig. 1(b) shows the photoluminescence excitation (PLE) spectrum obtained by monitoring the low-energy edge of the exciton luminescence. We observe that the exciton profile is produced in the PLE spectrum but is shifted slightly to higher energy. Also shown in Fig. 1(c) is the variation of the luminescence decay rate across the exciton line,
Periods x x x x x
15 10 10 10 10 x 1 xl xl
I
:
S6 40 A .
Cd0•33Zn0~67Te
(b) .~
(c) .....-
(a)
. ..~.
~...
214216218220
Energy (eV) Fig. 1. Photoluminescence (a) excitation spectrum (b) and luminescence decay time (c) for the 40 A Cd0 33Zn0 6~Te/ZnTe single quantum well (S6) taken at 10 K.
These results suggest that spectral diffusion of the excitons is occurring within the exciton profile. The absorption of light leads to the formation of excitons in regions of varying potential due to the alloy nature of the well material. Excitons created on the high-energy side of the exciton line can recombine radiatively where they were created or they can move to a different environment and therefore to a new spectral position within the exciton line where they can in turn either recombine or diffuse. The process of exciton movement within the exciton profile is called spectral diffusion. At the low temperatures of our experiments, the relaxation within the exciton line occurs through acoustic phonon assisted hopping [3] and
218
J.F. Donegan et al.
Journal oJ Luminescence 58 (1994) 216 222
will be predominantly to lower energy. The process of relaxation means that under steady-state conditions, states low in the exciton line will become more heavily populated than those higher up and so the peak position of the exciton line in luminescence is shifted from the peak in absorption. This shift in energy (1.0meV) has become known as the Stokes shift and it is a measure of the spectral diffusion within the exciton line. In Fig. 2 we present time-resolved luminescence spectra for the same SQW sample (S6). These spectra allow us to see the exciton profile as it evolves in time and thus to observe directly the process of spectral diffusion within the exciton line, In this figure the peak of the exciton at short times is indicated by a vertical line at 2.18 1 eV as a guide to the observation of spectral diffusion. After a time of 200 ps we observe that the exciton peak has shifted by about 1 meV to lower energy and that
S6:
40
X 1
X 1 8
For excitation energies far above the band gap, the exciton luminescence line shape is independent of pump position. In Fig. 3 we show two very
A
~ 97 Ps
4. Non-resonant fluorescence line narrowing At low temperatures, all samples show strong intrinsic excitonic luminescence. The width of the exciton luminescence line is similar to its width in absorption and ranges from 4 to 5 meV (HWHM). However, we find that in these samples the shape of the exciton luminescence line also depends on the wavelength position of the excitation source.
Cd33Zn,~7Te
0 ps
after this time no further shift of the line occurs. The Stokes shift of I meV is very similar to that observed in the steady-state spectra in Fig. 1. These time-resolved spectra show that spectral diffusion occurs within a time of 200 ps. The increase in the exciton decay rate from low- to high-energy side in the exciton profile is a result of the spectral diffusion process. As the excitons migrate to lower energy, further spectral relaxation becomes more difficult as the excitons become increasingly more localised by the alloy potential fluctuations. We note that the exciton recombination and spectral diffusion times are comparable and they indicate an overall slow rate of spectral relaxation within the exciton profile in Cd~Zn1 ~Te/ZnTe.
1~x86 S3 30 A Cd
i~—
A LO
Zn ~ Te wells
~
~“
_________
2.170
1
•~~_,_
2.175 Energy(eV)
2.190
Fig. 2. Time-resolved photoluminescence spectra for the 40 A Cd0,3 3Zn0 67Te/ZnTe single quantum well (S6) under 20 ps excitation. The spectra at different times are normalised showing the small change in line shape with time. The multiplication factor is shown on the right. The vertical line at 2.181 eV is a guide to the eye to show the gradual shift of the luminescence peak with increasing time,
°-
~
‘
LO”
2240
2 256
Energy (eV)
Fig. 3. Luminescence spectra for sample S3 30 A Cd0 25 Zn0 75Te ZnTe MQW structure with different pump energies; 2.268 (continuous line) and 2.28 1 eV (dashed line). Note the sharp lines labelled L01, LO, LO”, L02.
J.F. Donegan el a!.
different PL spectra for the
Journal of Luminescence 58 (1994) 216 222
30A Cd0 25Zn0 75Te/
ZnTe MQW sample (S3). The spectrum shown as a dashed line is similar to the normal exciton line shape. Compare this to the second PL spectrum shown in Fig. 3 as a solid line. Here the PL was excited using a narrow band laser just 20meV above the centre of the exciton line. At the middle of the exciton line, a prominent sharp line appears on top of the background luminescence. As the exciting laser is tuned, two sharp lines labelled LO (also seen weakly in the dashed-line spectrum) and L02 move across the exciton luminescence. The energy separation between these lines and the excitation laser stays constant regardless of the excitation energy and both lines only appear superimposed on the background exciton luminescence, The L01 line is shifted from the laser line by 25.6meV which we associate with the ZnTe-like LO phonon while line L02 is shifted 20.3 meV and is associated with the CdTe-like LO phonon in Cd~Zn1 ~Te. Although these assignments are the same as for resonant Raman scattering [5], we will show that the sharp lines are predominantly luminescent in nature at low temperature. The luminescence spectra of Fig. 3 show that excitons in different parts of the inhomogeneously broadened exciton luminescence behave differently and can be selectively probed. By monitoring a narrow spectral region in emission as in a luminescence excitation experiment, the creation and relaxation channels for a subset of excitons can be investigated. This is a form of fluorescence line narrowing (FLN). FLN normally occurs when an inhomogeneously broadened line is excited resonantly by a narrow band laser. Provided that there is little spectral relaxation across the line, the fluorescence originates only from the subset of states excited and is narrower than the full inhomogeneous line width. Our data on Cd~Zni ~Te/ZnTe quantum wells represent a different type of FLN in which the excitation is non-resonant with the emission. The process that forms the sharp lines is explained as follows: Consider narrow band pumping at an excitation energy. Ee~c E0 + nELO, where ELn is the LO-phonon energy, E0 is the exciton ground state energy in just one part of the inhomogeneous line and n is the phonon number (n 1 for the case in =
=
219
Fig. 3). The excitons created by the pumping have large momenta and are called ‘hot’ excitons. Hot excitons preferentially relax by LO-phonon emission to the ground state at k 0. This can create a narrow distribution of excitons because the energy of the participating LO phonons is well defined. Given a low rate of spectral diffusion, as discussed earlier, the excitons will remain in a narrow band for long enough to radiatively recombine, giving rise to a sharp line. There will also be a background luminescence signal because free carriers will also be created which relax non-preferentially into the exciton line. Hence we expect to see two sharp lines involving the L01 and L02 phonons. respectively, superimposed on a broader background luminescence (Fig. 3). In our quantum well materials the intrinsic luminescence is dominated by excitonic recombination. It is to be noted that lasing action has been observed in these materials at efficiencies equivalent to those found in high quality III V materials [6]. In addition, the spectral diffusion rate is low, as indicated by the small Stokes shift between excitation and emission (Fig. 1(a)). This allows the formation of sharp lines as detailed previously both with high radiative efficiencies and long lifetimes. As the sharp line modes are LO-phonon replicas, we must consider the possibility that they are due to resonant Raman scattering. There has always been some controversy over the distinction between resonant Raman scattering (RRS) and luminescence [4]. Raman scattering is a direct process involving virtual states, while luminescence is absorption into real states followed by emission. However, near-resonance real states can be involved in the scattering process and when phonon replicas are observed experimentally, their origin as luminescence or resonant Raman features may be ambiguous. Theory [7] indicates that a more correct view is to consider the phase (or transverse) relaxation time T2 and the energy (or longitudinal) relaxation time T1 for the material under study in so far as they can be defined. Resonant Raman scattering is considered to occur over a time T2 while luminescence occurs over a time T~. In the case that T2 is determined by T1, the distinction between the resonant Raman and luminescence processes becomes meaningless. T~ and T2 —
220
J.F. Donegan et al.
Journal of Luminescence 58 (1994) 216 222
can be measured in time-resolved experiments. At resonance, the ratio of the resonant Raman scattering to the luminescence is proportional to the ratio of the phase to the energy relaxation time such that I(Raman) I(Luminescence)
I
S6.40A —12.7meV
(1)
.E
For an exciton in a semiconductor, loss of coherence may arise from scattering with free carriers, other excitons, acoustic and optical phonons, lattice imperfections and other fluctuations in the crystal field. In our Cd~Zni ~Te/ZnTe quantum well structures, we have measured the lifetime of the excitons by time-resolved photoluminescence and their coherence decay time by time-resolved fourwave mixing. The results of these experiments show that the decay time of the sharp lines (115 ps) is similar to the decay of the underlying luminescence (120 ps) and that this decay time is much longer than the coherence time of the excitons (25 p5 measured by four-wave mixing on the low-energy side of the exciton absorption). Under the criterion that T2 << T1, we conclude that the sharp lines are predominantly luminescent in nature and are not due to resonant Raman scattering. Knowing the dephasing time is important if the problem of resonant Raman scattering versus luminescence is to be avoided and also because it is difficult to make assumptions on the values of dephasing times. Dephasing times can have a large range depending on the material.
~
cC
.
T
10 K
ph 70 K
1 150K
~ ~
290 K .
I
I
2.05
2.10
_______________________
2.15 Energy (eV)
2.20
Fig. 4 Photoluminescence spectra as a function of temperature for the 40 A Cd 33Zn57Te/ZnTe single quantum well sample (S6) showing the dominance offree exciton recombination upto room temperature.
high-energy tail due to free-carrier recombination. The SQW samples have the narrowest low-temperature line widths of our Cd~Zn1 ~Te/ZnTe samples as well as the weakest defect luminescence. These are the most recently grown samples and indicate that II VI materials are rapidly catching up on their III V counterparts in material quality. The main interaction that determines the thermal broadening is believed to be the scattering of excitons from K 0 states by LO phonons. This interaction homogeneously broadens the line with the homogeneous line width given by [9] /
(2)
-\
i E~0~
5. Thermal broadening of the exciton line by LO phonons As the temperature increases, the exciton absorption and PL lines broaden out. The extent of the thermal broadening varies with well material and also with well width [8]. In Fig. 4, we show the luminescence spectrum of the single quantum well (SQW) sample S6 as a function of temperature. This spectrum, as with all the SQW samples, is dominated by free exciton luminescence even up to room temperature. Note that the exciton line has broadened with increasing temperature and the exciton line at room temperature has a pronounced
explkT,
1
\
This is just the phonon interaction factor, [‘ph’ multiplied by the phonon occupation number, where EL0 is the LO-phonon energy and kT is the thermal energy. For all our samples the low-ternperature exciton line shapes are almost exactly Gaussian. The observed exciton line widths are a convolution of a Gaussian profile due to inhomogeneous broadening with the Lorentzian profile of the homogeneous line width. The resulting measured line shape has a Voigt profile and as it has no analytic expression, a numerical deconvolution procedure is required to determine the homogeneous line width. The fit to the HWHM widths
J.F. Donegan et a!.
gives
[‘ph
energy
/ Journal of Luminescence
as 12.7 meV using the ZnTe LO-phonon
ELO 26.1 meV. This compares to 5.5 meV in GaAs [10] and to ~‘ph 10.5 meV in In~Ga1 ~As quantum wells [11]. The thermal broadening depends on several factors. The smaller LO-phonon energy in these materials leads to higher phonon occupancy at room temperature than in either GaAs or In~Ga1 LAs. The phonon interaction factor [‘ph has two contributions: the Fröhlich parameter and an integral over possible scattering states. The Fröhlich parameter, ~ is a material parameter which decreases on going from pure ZnTe to pure CdTe and describes the strength of the LO-phonon electron interaction. The integral over scattering states depends non-linearly on the number of final states into which the excitons and the resulting electron hole pairs can scatter. In general, this decreases with increasing exciton binding energy. It should also decrease with decreasing well width as fewer electron and hole subbands become available within an LO-phonon energy of the exciton, on going to narrower wells. For the SQW samples we find [‘ph varies from 12.7meV for the 40A samples 17.0meV for the 70A sample to 19.0meV for the 100 A sample. Of the samples studied we find that the SQW sample with a 40A well and 33% Cd concentration has the smallest resulting [‘ph. From [8] we find that [‘ph can be reduced considerably if the exciton binding energy can exceed the LOphonon energy, a situation unique to II VI materials. This has led to the proposal of new optoelectronic II VI devices such as the room-temperature exciton laser, [‘ph
=
—
=
6. Exciton localisation The alloy nature of the CdZnTe material results in the formation of excitons in regions of potential fluctuations. Comparing the dephasing and spectral diffusion times with other materials allows us to form an impression of the extent of exciton localisation in our materials. At Helium temperatures. delocalised excitons lose phase rapidly through elastic scattering of impurities and interfaces as observed in GaAs SQWs (T2 2ps [11]) and through elastic scattering from alloy fluctu-
ations
58 (1994) 216 222
as
observed
221
in
In~Ga1 ~AsMQWs
(T2 0.5 Ps [12]). For localised excitons dephasing is usually associated with inelastic scattering and may be orders of magnitude slower. In In~Ga1 5As MQWs [13] acoustic phonon assisted tunnelling leading to spectral diffusion results in T2 3Ops, while in CdS5Se1 dephasing is almost lifetime limited with T2 times as long as 400ps [14]. These results indicate that for strongly localised excitons the spectral diffusion time is long and the dephasing time is determined by the diffusion time. For delocalised excitons, on the other hand, the dephasing time is very short, on the order of 1 ps. The observed dephasing time of 25ps in our samples indicates that the excitons are not delocalised and this is supported by the slow spectral diffusion rate. The fact that T2 is considerably less than the diffusion time indicates that our excitons are not completely localised. The excitons have a characteristic localisation length which is large enough to allow some dephasing by elastic scattering but small enough to prevent rapid spectral diffusion. ~,
7. Conclusion In this paper we have measured the optical properties of the lowest energy heavy-hole exciton in Cd~Zn1 5Te/ZnTe quantum well structures. We have measured the extent of spectral diffusion of excitons within the inhomogeneously broadened line by time-resolved luminescence. While there is some diffusion, it is weak and the excitons are localised at low temperature. This is borne out by the fact that there is very little shift of the luminescence peak from the absorption under steady-state conditions. We have also observed non-resonant fluorescence line narrowing in these materials in which the direct creation of hot excitons can lead to sharp lines sitting on top of the inhomogeneously broadened exciton line at low temperature. By a combination of picosecond time-resolved luminescence and four-wave mixing, we have measured T1 and T2 for the excitons and have identified the sharp lines as due to luminescence rather than resonant Raman scattering. The mechanism and strength of the thermal broadening of the exciton
222
iF. Donegan et al.
Journal of Luminescence 58 (1994) 216 222
has been measured up to room temperature. The extent of the exciton localisation can be deduced by a comparison of the dephasing and spectral diffusion times with other systems.
Acknowledgements It is a pleasure to acknowledge the contribution of the following people to our study: Dr. R.D. Feldman and Dr. R.F. Austin for growing these magnificent materials, Professor E.O. Göbel and Professor M.D. Sturge for helpful discussions, Dr. MO. Henry for the loan of cryogenic equipment, Dr. R. Fischer, Dr. J. Feldmann, and R. Hahn of the University of Marburg for help with the time-resolved luminescence experiments. References [1] R.P. Stanley, J. Hegarty, RD. Feldman and R.F. Austin, AppI. Phys. Lett. 53 (1988) 1417. [2] S. Permogorov, Phys. Stat. Sol. (b) 68 (1975) 9. [3] E. Cohen and M.D. Sturge, Phys. Rev. B 25 (1982) 3832.
[4] The arguments for and against this distinction are well summarised in the comment “Resonant Scattering or absorption followed by emission”, YR. Shen, Phys. Rev. B 14 (1976) 1772 and the reply by JR. Solin and H. Merkelo, Phys. Rev. B 14 (1976) 1775. [5] D.J. Olego, P.M. Racaah and J.P. Faurie, Phys. Rev. B 33 (1986) 3819. [6] AM. Glass, K. Tai, RB. Bylmsa, RD. Feldman, D.H. Olson and R.F. Austin, AppI. Phys. Lett. 53 (1988) 834. [7] Y. Toyozawa, J. Phys. Soc. Japan 41(1976) 400. [8] J.P. Doran, R.P. Stanley, J.F. Donegan, J. Hegarty, R. Fischer, E.O. Göbel, RD. Feldman and R.F. Austin, B 185and (1993) 566. Williams, Semiconductor and [9] Physica H.B. Bebbs E.H. Semimetals, ed. R.K. Williardson and AC. Beer (Academic Press, New York, 1972) p. 256. [10] DAB. Miller, D.S. Chemla, D.J. Eilenberger, P.W. Smith, AC. Gossard and W.T. Tsang, AppI. Phys. Lett. 41(1982) 679. [11] J.S. Weiner, D.S. Chemla, DAB. Miller, T.H. Wood, D. Silvo and Y. Cho, AppI. Phys. Lett. 46 (1985) 619. [12] L. Schultheis, A. Honold, J. KuhI, K. Kdhler and C.W. To, Phys. Rev. B 34 (1986) 9027. [13] M. Wegener, D.S. Chemla, S. Schmitt-Rink and W. Schafer, Phys. Rev. A 42 (1990) 5675. [14] J. Hegarty, K. Tai and W.T. Tsang, Phys. Rev. B 38 (1988) 7843. 1151 G. Noll, U. Siegner, E.O. Gbbel and S. Shevel, Phys. Rev. Lett. 64 (1990) 792.