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Resonance two-photon Raman scattering and luminescence of biexcitons in CuCl
Journal of Luminescence 18/19 (1979) 683—686 © North-Holland Publishing Company
RESONANCE TWO-PHOTON RAMAN SCATTERING AND LUMINESCENCE OF BIEXCITONS IN CuCI B. HONERLAGE*, A. BIVAS, VU DUY PHACH and J.B. GRUN Laboratoire de Spectroscopie et d’Optique du Corps Solide, Associé au C.N.R.S. no. 232. Université Louis Pasteur 5, rue de I’Université 67000 STRASBOURG, France
The two-photon Raman scattering via biexcitons gives the possibility to perform a spectroscopy of the excitonic polariton in momentum space by varying the experimental configuration. The polarization of the emitted light is compared to that of the biexciton luminescence. Thus, direct information on the biexciton distribution in momentum space is obtained.
In CuC1, biexcitons are created resonantly by two-photon absorption if the energy hw, of the exciting polaritons is equal to half the biexciton energy EB. These real biexcitons relax between themselves and with the lattice losing the memory of their conditions of creation. They recombine, emitting a lower polariton and leaving in the crystal, either a lower polariton, or an upper polariton, or a longitudinal exciton. This is a luminescence-like emission [1]. If the energy hw, of the exciting polaritons is detuned from the resonance, biexcitons are created only virtually, with a definite momentum equal to two times the momentum q, of these exciting polaritons. They recombine as the real biexcitons, but now, the momenta and energies of all the particles involved in the process are conserved. This is a Raman-like emission [2—5].This Raman process gives the possibility to perform a spectroscopy of the polariton in momentum space by varying the energy of the exciting photons or the scattering angle 6 between incoming and observed polaritons. Assuming that the polariton dispersion law E(q) is known, the momentum q,~ of the exciting polaritons is obtained from their energy hwj. The direction of propagation of these polaritons is deduced from the momentum dependent index of refraction n(Jq,I) and the angle of incidence a. Then, the momenta q and k of the two quasi particles created in the crystal as well as the scattering angle 6 can be computed self-consistently from n(~q,~) and from energy and momentum conservation 13,41 and [6,7]. In a backward scattering configuration, the scattering angle is large (6 1800). *
On leave from: Fachbereich Physik, Universität Regensburg, D 8400 Regensburg. 683
684
B. Honerlage et aL/Ra,nan scattering of biexcitons in CuCI
The lower polariton left in the crystal is then exciton-like. Its energy is almost equal to the energy of the transverse exciton ET. Therefore, as shown in fig. I, the polariton observed gives rise to the emission line RT, which, unlike the luminescence line N1, shifts in the spectrum twice more rapidly than the exciting photon energy as expected from energy conservation. The process, where a longitudinal exciton is left in the crystal, gives rise to the emission line RL which shifts in the spectrum as the RT line. In the forward scattering configuration, the scattering angle 6 is small. The final states of the transition to two lower polaritons are then in the bottleneck region of the polariton dispersion curve; their energy and momentum depend strongly on the scattering angle 6. For 6 < 30°, three different recombination channels exist for one given experimental configuration. Two of them (R~and RT) have been observed in our experiment, as shown in fig. 2, for a fixed photon energy hw, = 3.1856 eV and for different scattering angles. The third one has its energy inside the exciton absorption and is therefore strongly absorbed. If we attribute the measured energies of the Raman lines to the momenta computed as explained above, we obtain the dispersion relation of the lower polariton and of the longitudinal exciton with high accuracy. It is described by the following parameters [3—71. 4)eV, EL = (3.2080 ± 104)eV, ET = (3.2025 ± 10 m*=(2.5 ±0.3)m 0. The polarization properties of the Raman emission and of the biexciton luminescence have also been studied [81. Direct information on the biexciton distribution is obtained. In a four particle process like the Raman diffusion, all the momenta of the particles are well-defined. The transition probability can be 3.160
3.165
3170
3175 tiw(eV)
3.160
3.165
~
_
3.170
3.175~w(eV) __
A
3.1890 eV
___
~ 31854eV
~941~ 3920
3910
3900 )\(A~
3920
~ 3910
3900 ~(A’)
Fig. I. Emission spectra of CuCI in the backward scattering configuration for different energies hw~ of the exciting photons.
)
B. Hönerlage et a!. / Raman scattering of biexcitons in CuCI
3.170
3.180
685
3.190 ~~(eV
A
~J1iaser
Ti C
ct=10
R~ ~ I~
3910
3900
3890
3880 A(A)
Fig. 2. Emission spectra in the forward scattering configuration for a constant angle of observation and various angles of incidence a.
calculated as a function of the angle i~ of polarization of the observed light and of the scattering angle 6. (~= 0 corresponds to a direction of polarization of the light perpendicular to the scattering plane). In fig. 3, the relative intensities of the Raman lines RT and RL are represented as functions of i~, for two different energies of the exciting photons. The solid lines give the theoretical variations. The agreement is good. It is interesting to compare these results to those obtained at the resonance (11w, = EB/2). In that case, it is no longer possible to distinguish between the luminescence and the Raman emission from their energetic position. The polarization properties are shown in fig. 4. The total emission N1 + RT shows no observable polarization effect; the NL + RL emission only a small one. The solid
I O~~o,o~oo:~
P1
x ~i~,=3.18ô6~V 0.5
t~RL 0
o
~i~j3.1863eV
90~
Fig. 3. Normalized intensities of the Raman emission lines R1 and angle ~, for different energies of the exciting photons.
18O~ RL
as functions of the polarization
B. HOnerlage et a!. / Roman scattering of biexcitons in CuC!
686
~
0.5~9 0
0
0
~
~ c
C)
90
180° t~
Fig. 4. Normalized intensities of the biexciton emission lines NT + R the polarization angle sj, for hw1 1/10 = 0.2 and 0: J/1~= 0.4).
=
E5/2
=
1 and N1 + R1 as functions of 3.1860eV and for different excitation intensities (X:
curves represent the polarization effects expected for both emissions, if the biexcitons had kept the momentum of their creation. We can, therefore, conclude that the really created biexcitons undergo elastic or inelastic scattering processes and thus have a distribution extended in momentum space hut confined in energy to the bottom of the band. The small rate of polarization of the NL + R1 emission is probably due to the recombination of some biexcitons. which have not yet undergone any relaxation process. In our configuration, it should not show up in the NT + RT emission. These results confirm our previous hypothesis about the formation of a cold gas of biexcitons [1].
References Ill R. Levy, C. Klingshirn. E. Ostertag, Vu Duy Phach and J.B. (3run, Phys. Stat. Sol. (h) 77 (1976) 381. [2] N. Nagasawa. T. Mita and M. Ueta, J. Phys. Soc. (Japan) 42 (1976) 929. [31B. Honerlage, Vu Duy Phach, A. Bivas and E. Ostertag. Phys. Stat. Sol. (b) 83 (1977) Kb). 14] Vu Duy Phach. A. Bivas. B. Honerlage and J.B. Grun. Phys. Stat. Sol. (h) 86 (1978) 199. [5] T. Itoh, T. Suzuki and M. Ueta. J. Phys. Soc. (Japan) 42 (1977) 1069. [6] E. Ostertag, These. Strasbourg (1977). 171 E. Ostertag. A. Bivas and J.B. Grun. Phys. Stat. Sol. (h) 84(1977) 673. [81 B. Honerlage. Vu Duy Phach and J.B. Grun. Phys. Stat. Sob. (b) 88 (1978) to he published. 191 F. Henneberger, K. Henneherger and J. Voigt Phys. Stat. Sol. (h) 83 (1977) 439.
RESONANCE TWO-PHOTON RAMAN SCATTERING AND LUMINESCENCE OF BIEXCITONS IN CuCI B. HONERLAGE*, A. BIVAS, VU DUY PHACH and J.B. GRUN Laboratoire de Spectroscopie et d’Optique du Corps Solide, Associé au C.N.R.S. no. 232. Université Louis Pasteur 5, rue de I’Université 67000 STRASBOURG, France
The two-photon Raman scattering via biexcitons gives the possibility to perform a spectroscopy of the excitonic polariton in momentum space by varying the experimental configuration. The polarization of the emitted light is compared to that of the biexciton luminescence. Thus, direct information on the biexciton distribution in momentum space is obtained.
In CuC1, biexcitons are created resonantly by two-photon absorption if the energy hw, of the exciting polaritons is equal to half the biexciton energy EB. These real biexcitons relax between themselves and with the lattice losing the memory of their conditions of creation. They recombine, emitting a lower polariton and leaving in the crystal, either a lower polariton, or an upper polariton, or a longitudinal exciton. This is a luminescence-like emission [1]. If the energy hw, of the exciting polaritons is detuned from the resonance, biexcitons are created only virtually, with a definite momentum equal to two times the momentum q, of these exciting polaritons. They recombine as the real biexcitons, but now, the momenta and energies of all the particles involved in the process are conserved. This is a Raman-like emission [2—5].This Raman process gives the possibility to perform a spectroscopy of the polariton in momentum space by varying the energy of the exciting photons or the scattering angle 6 between incoming and observed polaritons. Assuming that the polariton dispersion law E(q) is known, the momentum q,~ of the exciting polaritons is obtained from their energy hwj. The direction of propagation of these polaritons is deduced from the momentum dependent index of refraction n(Jq,I) and the angle of incidence a. Then, the momenta q and k of the two quasi particles created in the crystal as well as the scattering angle 6 can be computed self-consistently from n(~q,~) and from energy and momentum conservation 13,41 and [6,7]. In a backward scattering configuration, the scattering angle is large (6 1800). *
On leave from: Fachbereich Physik, Universität Regensburg, D 8400 Regensburg. 683
684
B. Honerlage et aL/Ra,nan scattering of biexcitons in CuCI
The lower polariton left in the crystal is then exciton-like. Its energy is almost equal to the energy of the transverse exciton ET. Therefore, as shown in fig. I, the polariton observed gives rise to the emission line RT, which, unlike the luminescence line N1, shifts in the spectrum twice more rapidly than the exciting photon energy as expected from energy conservation. The process, where a longitudinal exciton is left in the crystal, gives rise to the emission line RL which shifts in the spectrum as the RT line. In the forward scattering configuration, the scattering angle 6 is small. The final states of the transition to two lower polaritons are then in the bottleneck region of the polariton dispersion curve; their energy and momentum depend strongly on the scattering angle 6. For 6 < 30°, three different recombination channels exist for one given experimental configuration. Two of them (R~and RT) have been observed in our experiment, as shown in fig. 2, for a fixed photon energy hw, = 3.1856 eV and for different scattering angles. The third one has its energy inside the exciton absorption and is therefore strongly absorbed. If we attribute the measured energies of the Raman lines to the momenta computed as explained above, we obtain the dispersion relation of the lower polariton and of the longitudinal exciton with high accuracy. It is described by the following parameters [3—71. 4)eV, EL = (3.2080 ± 104)eV, ET = (3.2025 ± 10 m*=(2.5 ±0.3)m 0. The polarization properties of the Raman emission and of the biexciton luminescence have also been studied [81. Direct information on the biexciton distribution is obtained. In a four particle process like the Raman diffusion, all the momenta of the particles are well-defined. The transition probability can be 3.160
3.165
3170
3175 tiw(eV)
3.160
3.165
~
_
3.170
3.175~w(eV) __
A
3.1890 eV
___
~ 31854eV
~941~ 3920
3910
3900 )\(A~
3920
~ 3910
3900 ~(A’)
Fig. I. Emission spectra of CuCI in the backward scattering configuration for different energies hw~ of the exciting photons.
)
B. Hönerlage et a!. / Raman scattering of biexcitons in CuCI
3.170
3.180
685
3.190 ~~(eV
A
~J1iaser
Ti C
ct=10
R~ ~ I~
3910
3900
3890
3880 A(A)
Fig. 2. Emission spectra in the forward scattering configuration for a constant angle of observation and various angles of incidence a.
calculated as a function of the angle i~ of polarization of the observed light and of the scattering angle 6. (~= 0 corresponds to a direction of polarization of the light perpendicular to the scattering plane). In fig. 3, the relative intensities of the Raman lines RT and RL are represented as functions of i~, for two different energies of the exciting photons. The solid lines give the theoretical variations. The agreement is good. It is interesting to compare these results to those obtained at the resonance (11w, = EB/2). In that case, it is no longer possible to distinguish between the luminescence and the Raman emission from their energetic position. The polarization properties are shown in fig. 4. The total emission N1 + RT shows no observable polarization effect; the NL + RL emission only a small one. The solid
I O~~o,o~oo:~
P1
x ~i~,=3.18ô6~V 0.5
t~RL 0
o
~i~j3.1863eV
90~
Fig. 3. Normalized intensities of the Raman emission lines R1 and angle ~, for different energies of the exciting photons.
18O~ RL
as functions of the polarization
B. HOnerlage et a!. / Roman scattering of biexcitons in CuC!
686
~
0.5~9 0
0
0
~
~ c
C)
90
180° t~
Fig. 4. Normalized intensities of the biexciton emission lines NT + R the polarization angle sj, for hw1 1/10 = 0.2 and 0: J/1~= 0.4).
=
E5/2
=
1 and N1 + R1 as functions of 3.1860eV and for different excitation intensities (X:
curves represent the polarization effects expected for both emissions, if the biexcitons had kept the momentum of their creation. We can, therefore, conclude that the really created biexcitons undergo elastic or inelastic scattering processes and thus have a distribution extended in momentum space hut confined in energy to the bottom of the band. The small rate of polarization of the NL + R1 emission is probably due to the recombination of some biexcitons. which have not yet undergone any relaxation process. In our configuration, it should not show up in the NT + RT emission. These results confirm our previous hypothesis about the formation of a cold gas of biexcitons [1].
References Ill R. Levy, C. Klingshirn. E. Ostertag, Vu Duy Phach and J.B. (3run, Phys. Stat. Sol. (h) 77 (1976) 381. [2] N. Nagasawa. T. Mita and M. Ueta, J. Phys. Soc. (Japan) 42 (1976) 929. [31B. Honerlage, Vu Duy Phach, A. Bivas and E. Ostertag. Phys. Stat. Sol. (b) 83 (1977) Kb). 14] Vu Duy Phach. A. Bivas. B. Honerlage and J.B. Grun. Phys. Stat. Sol. (h) 86 (1978) 199. [5] T. Itoh, T. Suzuki and M. Ueta. J. Phys. Soc. (Japan) 42 (1977) 1069. [6] E. Ostertag, These. Strasbourg (1977). 171 E. Ostertag. A. Bivas and J.B. Grun. Phys. Stat. Sol. (h) 84(1977) 673. [81 B. Honerlage. Vu Duy Phach and J.B. Grun. Phys. Stat. Sob. (b) 88 (1978) to he published. 191 F. Henneberger, K. Henneherger and J. Voigt Phys. Stat. Sol. (h) 83 (1977) 439.