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ZnSSe quantum wells by four-wave mixing
JOURNAL OF
LUMINESCENCE Journal of Luminescence 66&67 (1996) 429-432
ELSEWIER
Coherent formation of biexcitons in ZnSe/ZnSSe quantum wells by four-wave mixing T. Kuroda”‘b’*, K. Inoue”, R. Kuribayashi”, F. Minamib, A. Mysyrowicz”, I. Suemunea *ResearchInstitutr “Depavtment
of Applied
’ Lahoratoiw
f&r- Electronic
Physics,
d’Optique
Srirncr.
Hokkaido
Tohyo Institute qf Technology.
Appliqu&
ENSTA. E&e
Uniwrsi
060. Japan
Megum.
Tolqo 1517. Japun
Pol>~technique. F-91 120 Palaiseau,
France
Abstract We confirm the existence of a biexciton in ZnSe-based quantum wells using transient four-wave-mixing spectroscopy. It is found that a new spectral line appears below the heavy-hole-related exciton resonance, corresponding to the excitonPbiexciton transition. Through the analysis, we have determined the dephasing time of the biexciton, as well as the biexciton binding energy.
1. Introduction It is well known that the optical nonlinearity of semiconductors is greatly enhanced by the appearance of a biexciton level. Biexcitonic effects are particularly interesting in II-VI quantum wells (QW), because of the large exciton oscillator strength compared to that for a bulk or GaAsbased QW. Although several studies have been reported on biexcitonic effects in ZnSe-based QW [l, 21, those experiments have been mostly based on a linear optical technique, such as a photoluminescence spectroscopy (PL). However, since a biexciton arises originally from a multi-photon excitation process, nonlinear spectroscopy is a most suitable and effective tool to investigate biexcitonic phenomena. In the present paper, we show evidence of biexciton formation in ZnSe/ZnS,Se, _x (x = 0.18) QW
* Corresponding author 0022-23
13/96/$15.00
SSDI 0022-23
,c:
1996
13(95)00184-O
using subpicosecond four-wave-mixing (FWM) spectroscopy. We clarify the contribution of biexcitonic resonance to the FWM emission, by resolving the FWM signal spectrally. Through the analysis, we determine a dephasing time for the biexciton.
2. Experimental We examined two samples of ZnSe/ZnS,Se,_X (x = 0.18) multiple QW with different thicknesses. They were grown on a (100) GaAs substrate by atmospheric pressure metalorganic vapor0 phase epitaxy, and cons@ted of 80 periods of a 50-A ZnSe well and a 50-A ZnS0,1sSe,.8a barrier for on,e sample, and 40 periods of a 94-A QW and a 94-A barrier for the other. Since similar results have been obtaineg for these0 two samples, the result for the 50-A ZnSe/SO-A ZnSSe QW has been mainly
Elsevier Science B.V. All rights reserved
described in this report. These samples were carefully characterized by PL and PL excitation (PLE) spectroscopy. The Stokes shift between the PL and PLE spectra for the lowest heavy-hole related (hh) exciton was found to be less than 0.3 meV, which is smaller than the linewidth in the PLE spectrum, _ 1.5 meV. This fact indicates that the present exciton line is broadened, predominantly by homogeneous broadening. Such a high-quality characteristic was also found in the reflectance spectra, which reveal a one-monolayer-terraced structure of QW layers [3]. The excitation source was the second-harmonic light from a mode-locked titanium-sapphire laser, producing pulses of 150 fs duration with a spectral width of 21 meV. FWM signals were measured adopting a reflectance geometry at the Brewster angle of incidence, allowing one to observe the signal with high signal-to-noise ratio. The excitation intensity was around 40 nJ/cm2 per pulse, which is a sufficiently low power level. All measurements were performed at 5 K.
3. Results In Fig. I. spectra of FWM signals are shown for different delay times, T, between the two pulses. The sign of T is defined as positive when a pulse with wave vector of kl precedes a pulse with k2, and we observe the signal emitted in the direction of - kl + 2k2. All the spectra are normalized to the maximum intensity. Several split lines are clearly found, denoted as the X (2.8161 eV), M (2.8115 eV), and A (2.8 187 eV). The dominant peak of the X line is assigned to the hh-related exciton line, and the A line should correspond to the hh exciton confined in the QW of different thickness, since the energy separation between the A- and X-lines are found to agree well with a calculated value based on a Kronig-Penny model, as is reported in Ref. [3]. The M line, seen on the lower energy side of the hh exciton, appears only for negative delays, and vanishes for positive delays. It is well known that the emission of FWM signals at negative delays arises from many-exciton effects, including a biexciton formation process. This is confirmed by results of PL spectroscopy for various pumping
2.8
Fig. I. Spectra times, together
2.81 2.82 ENERGY (eV)
2.83
of four-nave-mixing signals at various with that of the excitation pulse.
delay
powers, as is shown in Fig. 2. Two contributions to the PL are observed; the respective lines coincide well in energy with each of the M and X lines in the FWM signals. The PL intensity of the M line is found to increase faster than linear with respect to the X line. Thus, we can conclude that the M line seen in the FWM signal corresponds to the transition from a biexciton to an exciton (M transition), and the binding energy for the biexciton is 4.6 (k 0.3) meV. In Fig. 3, we show the variation of the FWM intensities as a function of T. detected at various spectral positions. In Fig. 3(a). the spectral window is tuned to the X line, and the results indicate deep modulation and an additional signal for negative delays. The temporal oscillation should be due to quantum beats between a hh and light-hole-related (lh) exciton. However, as the window is tuned to the M line, the signal is found to almost disappear for T > 0, and with decreasing T. it rises steeply after T = 0, and then decays. This temporal feature can be interpreted by considering a two-photon resonant FWM process involving exciton and biexciton levels: The preceding pulse with k, excites a biexciton state of mode 2k2 through the two-photon resonant transition. The coherent biexciton diffracts the delayed pulse with k,, in the direction signal. Thus, the of - k, + 2k2 as a FWM decaying feature should reflect the phase relaxation of a biexciton state, as will be discussed below.
T. Kwodu
rt al. i Journcrl of Luminescence
431
66& 67 (I 996) 429-432
sponse involving exciton and biexciton states. Calculations are based on a third-order perturbation treatment of the optical Bloch equations for a four-level system, following the one first introduced in Ref. [S]. The induced polarization P for negative delays can be expressed as follows: P(t) ‘Z O( - T) @(t - I ,)exp(TT) 2.79
2.8
2.82 2.81 ENERGY (eV)
x (exp([iSZx - ;‘xl[f -
2.83
-
Fig. 2. Photoluminescence spectra for different excitation intensities. The peak power is (a) 22.4 kW/cm’. (b) 1.85 kW.‘cm’. and (cl 116 W!cm’. The pulse width is s 40 ns.
0
1
2
DELAY TIME (ps) Fig. 3. FWM intensities as a function of delay times detected (a) 2.8161 eV. (h) 2.81 15 CV and (c) 2.8187 eV.
at
It is noted that the FWM signal for the A line also shows an unexpected feature of a slow rising of the signal. This could be caused by polarization interference between excitons in QWs of onemonolayer different thickness [4]. However, we will not consider it in further detail.
4. Discussion In order to interpret the decaying profile at negative delays, we have calculated the nonlinear re-
exp([i%
r,l)
- ;*hll[t - r,])).
(1)
where 0 represents the step function; t,, the incident time of the delayed pulse; s2xtM,, the exciton (exciton-biexciton) transition energy; ;‘x, Ye, and r, the phase relaxation rates for the ground-exciton, exciton-biexciton and ground-biexciton transitions, respectively. This model is based on a system with two excitons, and if there is no correlation between excitons, i.e., Qx = sZM, and ;lx = yM, the signal disappears. Thus, the signal for negative delays reflects the interaction between excitons, and the new emission line at QM corresponds to the renormalized energy for two correlated excitons, that is, the biexciton. Eq. (1) shows that the decay of a FWM intensity for negative delays depends only on the biexciton dephasing rate, r. Thus, we can estimate the dephasing time for biexcitons (the inverse of r), as _ 0.3 ps. and for excitons as - 0.6 ps. The enhancement of a dephasing rate for the biexciton should reflect the intrinsic nature of biexciton dynamics. It is noted that a similar feature with r = 2;lx could be expected in a simple model based on the semiconductor Bloch equations (SBE) [6]. However, we extracted a value of r from the FWM signal for the M line, which could not be influenced by the SBE induced effects. Thus. the r obtained through the present treatment should directly provide microscopic information on biexciton dynamics. Although Eq. (1) shows that the amplitude of the oscillator for !Zx is equal to that for !&, the observed intensity for the X line is around eight times larger than the M line, as is shown in Fig. 1. This is considered to be caused by other many-exciton effects, such as a local field correction, which is neglected in our treatment. Recently. Fischer et al. [7] reported that the FWM signal in
432
T. Kuroda et al. ! Journal
cfLuminescence 66&67
ZnSe QWs is much stronger than that in GaAs QWs, reflecting strong many-exciton interactions, and the system should be described in terms of the SBE. Our observation indicates that, in order to describe coherent transients in ZnSe QWs correctly, the comprehensive treatment of many-exciton effects taking account of biexciton formation is needed.
5. Conclusions We confirm the formation of biexcitons in ZnSe quantum wells by observing the coherent emission of a nonlinear signal corresponding to the biexcitonexciton transition. We observe the phase relaxation of the biexciton state from the fourwave-mixing signal.
Acknowledgement This work is supported in part by a Grant-in-Aid for the International Scientific Program from the
Ministry Japan.
(1996) 429--432
of Education,
Science
and
Culture
of
References [1] Q. Fu, A. Mysyrowicz, A.V. Nurmikko, R.L. Gunshor and L.A. Kolodziejski, Phys. Rev. B 37 (1988) 8791. [2] K. Inoue, K. Yoshida, A. Mysyrowicz and A. Yamanaka, m: &VI Compounds and Semimagnetic Semicond., eds. H. Heinrech et al. (Trans. Tech. Publications, Switzerland, 1995) p. 219. [3] K. Inoue. T. Kuroda, K. Yoshida and I. Suemune. Appl. Phys. Lett. 65 (1994) 2830. [4] T. Kuroda, K. Inoue, I. Suemune, R. Kuribayashi and F. Minami, in: Proc. 22nd Int. Conf. on the Physics of Semiconductors, ed. D.J. Lockwood (World Scientific. Singapore, 1995) p. 1388. [5] G. Finkelstein, S. Bar-Ad, 0. Carmel, 1. Bar-Joseph and Y. Levinson. Phys. Rev. B 47 (I 993) 12 964. [6] M. Wegener. D.S. Chemla, S. Schmitt-Rink and W. Shafer. Phys. Rev. A 42 (1990)5675. [7] A.J. Fischer, D.S. Kim, J. Hays, W. Shari.. J.J. Song, D.B. Eason, J. Ren, J.F. Schetzina, H. Luo, J.K. Furdyna, Z.Q. Zhu, T. Yao. J.F. Klem and W. Shafer, Phys. Rev. Lett. 73 (1994) 2368.
LUMINESCENCE Journal of Luminescence 66&67 (1996) 429-432
ELSEWIER
Coherent formation of biexcitons in ZnSe/ZnSSe quantum wells by four-wave mixing T. Kuroda”‘b’*, K. Inoue”, R. Kuribayashi”, F. Minamib, A. Mysyrowicz”, I. Suemunea *ResearchInstitutr “Depavtment
of Applied
’ Lahoratoiw
f&r- Electronic
Physics,
d’Optique
Srirncr.
Hokkaido
Tohyo Institute qf Technology.
Appliqu&
ENSTA. E&e
Uniwrsi
060. Japan
Megum.
Tolqo 1517. Japun
Pol>~technique. F-91 120 Palaiseau,
France
Abstract We confirm the existence of a biexciton in ZnSe-based quantum wells using transient four-wave-mixing spectroscopy. It is found that a new spectral line appears below the heavy-hole-related exciton resonance, corresponding to the excitonPbiexciton transition. Through the analysis, we have determined the dephasing time of the biexciton, as well as the biexciton binding energy.
1. Introduction It is well known that the optical nonlinearity of semiconductors is greatly enhanced by the appearance of a biexciton level. Biexcitonic effects are particularly interesting in II-VI quantum wells (QW), because of the large exciton oscillator strength compared to that for a bulk or GaAsbased QW. Although several studies have been reported on biexcitonic effects in ZnSe-based QW [l, 21, those experiments have been mostly based on a linear optical technique, such as a photoluminescence spectroscopy (PL). However, since a biexciton arises originally from a multi-photon excitation process, nonlinear spectroscopy is a most suitable and effective tool to investigate biexcitonic phenomena. In the present paper, we show evidence of biexciton formation in ZnSe/ZnS,Se, _x (x = 0.18) QW
* Corresponding author 0022-23
13/96/$15.00
SSDI 0022-23
,c:
1996
13(95)00184-O
using subpicosecond four-wave-mixing (FWM) spectroscopy. We clarify the contribution of biexcitonic resonance to the FWM emission, by resolving the FWM signal spectrally. Through the analysis, we determine a dephasing time for the biexciton.
2. Experimental We examined two samples of ZnSe/ZnS,Se,_X (x = 0.18) multiple QW with different thicknesses. They were grown on a (100) GaAs substrate by atmospheric pressure metalorganic vapor0 phase epitaxy, and cons@ted of 80 periods of a 50-A ZnSe well and a 50-A ZnS0,1sSe,.8a barrier for on,e sample, and 40 periods of a 94-A QW and a 94-A barrier for the other. Since similar results have been obtaineg for these0 two samples, the result for the 50-A ZnSe/SO-A ZnSSe QW has been mainly
Elsevier Science B.V. All rights reserved
described in this report. These samples were carefully characterized by PL and PL excitation (PLE) spectroscopy. The Stokes shift between the PL and PLE spectra for the lowest heavy-hole related (hh) exciton was found to be less than 0.3 meV, which is smaller than the linewidth in the PLE spectrum, _ 1.5 meV. This fact indicates that the present exciton line is broadened, predominantly by homogeneous broadening. Such a high-quality characteristic was also found in the reflectance spectra, which reveal a one-monolayer-terraced structure of QW layers [3]. The excitation source was the second-harmonic light from a mode-locked titanium-sapphire laser, producing pulses of 150 fs duration with a spectral width of 21 meV. FWM signals were measured adopting a reflectance geometry at the Brewster angle of incidence, allowing one to observe the signal with high signal-to-noise ratio. The excitation intensity was around 40 nJ/cm2 per pulse, which is a sufficiently low power level. All measurements were performed at 5 K.
3. Results In Fig. I. spectra of FWM signals are shown for different delay times, T, between the two pulses. The sign of T is defined as positive when a pulse with wave vector of kl precedes a pulse with k2, and we observe the signal emitted in the direction of - kl + 2k2. All the spectra are normalized to the maximum intensity. Several split lines are clearly found, denoted as the X (2.8161 eV), M (2.8115 eV), and A (2.8 187 eV). The dominant peak of the X line is assigned to the hh-related exciton line, and the A line should correspond to the hh exciton confined in the QW of different thickness, since the energy separation between the A- and X-lines are found to agree well with a calculated value based on a Kronig-Penny model, as is reported in Ref. [3]. The M line, seen on the lower energy side of the hh exciton, appears only for negative delays, and vanishes for positive delays. It is well known that the emission of FWM signals at negative delays arises from many-exciton effects, including a biexciton formation process. This is confirmed by results of PL spectroscopy for various pumping
2.8
Fig. I. Spectra times, together
2.81 2.82 ENERGY (eV)
2.83
of four-nave-mixing signals at various with that of the excitation pulse.
delay
powers, as is shown in Fig. 2. Two contributions to the PL are observed; the respective lines coincide well in energy with each of the M and X lines in the FWM signals. The PL intensity of the M line is found to increase faster than linear with respect to the X line. Thus, we can conclude that the M line seen in the FWM signal corresponds to the transition from a biexciton to an exciton (M transition), and the binding energy for the biexciton is 4.6 (k 0.3) meV. In Fig. 3, we show the variation of the FWM intensities as a function of T. detected at various spectral positions. In Fig. 3(a). the spectral window is tuned to the X line, and the results indicate deep modulation and an additional signal for negative delays. The temporal oscillation should be due to quantum beats between a hh and light-hole-related (lh) exciton. However, as the window is tuned to the M line, the signal is found to almost disappear for T > 0, and with decreasing T. it rises steeply after T = 0, and then decays. This temporal feature can be interpreted by considering a two-photon resonant FWM process involving exciton and biexciton levels: The preceding pulse with k, excites a biexciton state of mode 2k2 through the two-photon resonant transition. The coherent biexciton diffracts the delayed pulse with k,, in the direction signal. Thus, the of - k, + 2k2 as a FWM decaying feature should reflect the phase relaxation of a biexciton state, as will be discussed below.
T. Kwodu
rt al. i Journcrl of Luminescence
431
66& 67 (I 996) 429-432
sponse involving exciton and biexciton states. Calculations are based on a third-order perturbation treatment of the optical Bloch equations for a four-level system, following the one first introduced in Ref. [S]. The induced polarization P for negative delays can be expressed as follows: P(t) ‘Z O( - T) @(t - I ,)exp(TT) 2.79
2.8
2.82 2.81 ENERGY (eV)
x (exp([iSZx - ;‘xl[f -
2.83
-
Fig. 2. Photoluminescence spectra for different excitation intensities. The peak power is (a) 22.4 kW/cm’. (b) 1.85 kW.‘cm’. and (cl 116 W!cm’. The pulse width is s 40 ns.
0
1
2
DELAY TIME (ps) Fig. 3. FWM intensities as a function of delay times detected (a) 2.8161 eV. (h) 2.81 15 CV and (c) 2.8187 eV.
at
It is noted that the FWM signal for the A line also shows an unexpected feature of a slow rising of the signal. This could be caused by polarization interference between excitons in QWs of onemonolayer different thickness [4]. However, we will not consider it in further detail.
4. Discussion In order to interpret the decaying profile at negative delays, we have calculated the nonlinear re-
exp([i%
r,l)
- ;*hll[t - r,])).
(1)
where 0 represents the step function; t,, the incident time of the delayed pulse; s2xtM,, the exciton (exciton-biexciton) transition energy; ;‘x, Ye, and r, the phase relaxation rates for the ground-exciton, exciton-biexciton and ground-biexciton transitions, respectively. This model is based on a system with two excitons, and if there is no correlation between excitons, i.e., Qx = sZM, and ;lx = yM, the signal disappears. Thus, the signal for negative delays reflects the interaction between excitons, and the new emission line at QM corresponds to the renormalized energy for two correlated excitons, that is, the biexciton. Eq. (1) shows that the decay of a FWM intensity for negative delays depends only on the biexciton dephasing rate, r. Thus, we can estimate the dephasing time for biexcitons (the inverse of r), as _ 0.3 ps. and for excitons as - 0.6 ps. The enhancement of a dephasing rate for the biexciton should reflect the intrinsic nature of biexciton dynamics. It is noted that a similar feature with r = 2;lx could be expected in a simple model based on the semiconductor Bloch equations (SBE) [6]. However, we extracted a value of r from the FWM signal for the M line, which could not be influenced by the SBE induced effects. Thus. the r obtained through the present treatment should directly provide microscopic information on biexciton dynamics. Although Eq. (1) shows that the amplitude of the oscillator for !Zx is equal to that for !&, the observed intensity for the X line is around eight times larger than the M line, as is shown in Fig. 1. This is considered to be caused by other many-exciton effects, such as a local field correction, which is neglected in our treatment. Recently. Fischer et al. [7] reported that the FWM signal in
432
T. Kuroda et al. ! Journal
cfLuminescence 66&67
ZnSe QWs is much stronger than that in GaAs QWs, reflecting strong many-exciton interactions, and the system should be described in terms of the SBE. Our observation indicates that, in order to describe coherent transients in ZnSe QWs correctly, the comprehensive treatment of many-exciton effects taking account of biexciton formation is needed.
5. Conclusions We confirm the formation of biexcitons in ZnSe quantum wells by observing the coherent emission of a nonlinear signal corresponding to the biexcitonexciton transition. We observe the phase relaxation of the biexciton state from the fourwave-mixing signal.
Acknowledgement This work is supported in part by a Grant-in-Aid for the International Scientific Program from the
Ministry Japan.
(1996) 429--432
of Education,
Science
and
Culture
of
References [1] Q. Fu, A. Mysyrowicz, A.V. Nurmikko, R.L. Gunshor and L.A. Kolodziejski, Phys. Rev. B 37 (1988) 8791. [2] K. Inoue, K. Yoshida, A. Mysyrowicz and A. Yamanaka, m: &VI Compounds and Semimagnetic Semicond., eds. H. Heinrech et al. (Trans. Tech. Publications, Switzerland, 1995) p. 219. [3] K. Inoue. T. Kuroda, K. Yoshida and I. Suemune. Appl. Phys. Lett. 65 (1994) 2830. [4] T. Kuroda, K. Inoue, I. Suemune, R. Kuribayashi and F. Minami, in: Proc. 22nd Int. Conf. on the Physics of Semiconductors, ed. D.J. Lockwood (World Scientific. Singapore, 1995) p. 1388. [5] G. Finkelstein, S. Bar-Ad, 0. Carmel, 1. Bar-Joseph and Y. Levinson. Phys. Rev. B 47 (I 993) 12 964. [6] M. Wegener. D.S. Chemla, S. Schmitt-Rink and W. Shafer. Phys. Rev. A 42 (1990)5675. [7] A.J. Fischer, D.S. Kim, J. Hays, W. Shari.. J.J. Song, D.B. Eason, J. Ren, J.F. Schetzina, H. Luo, J.K. Furdyna, Z.Q. Zhu, T. Yao. J.F. Klem and W. Shafer, Phys. Rev. Lett. 73 (1994) 2368.