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Magnetoluminescence studies of excitonic scattering processes in high purity GaAs
Solid State Communications, Vol. 17, pp. 1185-1188, 1975.
Pergamon Press.
Printed in Great Britain
MAGNETOLUMINESCENCE STUDIES OF EXCITONIC SCATTERING PROCESSES IN HIGH PURITY GaAs E. G6bel,* K.L. Shaklee and R. Epworth Bell Telephone Laboratories, Holmdel, NJ 07733, U.S.A.
(Received 18 June 1975 by A.G. Chynoweth)
The broad emission line at about 1.512 eV, which dominates the emission spectra of pure GaAs at intermediate excitation levels (1-300 kW/cm 2 ) and low temperatures (< 40 K) is investigated in magnetic fields up to magnetic flux densities of 10 T. The shift of the emission maximum in the magnetic field is exactly the same as recently reported for the free exciton. This demonstrates that at high excitation levels exciton-electron scattering is the dominant mechanism for the radiative decay of free excitons.
THE LUMINESCENCE spectra of pure GaAs at low temperatures change considerably at high pumping levels. One of the characteristic features of the "high intensity" luminescence is the occurrence of a broad emission line at about 1.52 eV (A-line) (the energetic position depends slightly on excitation power), which dominates the spectra at intermediate excitation levels ("- 1-300 kW/cm 2). Based on energetic arguments, 1' a, s lineshape fits s and on the results of the electric field,a doping s and temperature dependence, 1 as well as excitation spectroscopy results 2 this emission line is interpreted in terms of excitonic scattering processes. However, up to now no clear choice between excitonexciton or exciton-electron scattering as the dominant mechanism for the radiative decay of free excitons at these high excitation levels could be made. All other radiative recombination channels for the free exciton (i.e. direct recombination of the exciton-polariton 4 at 1.5157 eV and 1.5146 eV in our samples and the LO-phonon replica at about 1.479 eV 5) are less important at the excitation powers discussed in this paper as can be shown by a comparison of the integrated emission intensities. In this paper we report on magnetohiminescence *Permanent address: Physikalisches Institut, University of Stuttgart, DTO00 Stuttgart 80, Pfaffenwaldring 58, Fed. Rep. Germany. 1185
studies of the A-line in magnetic fields up to flux densities of 10 T. Additionally the experimental data are compared with recent magnetoluminescence results for the free exciton.6 This comparison clearly shows that exciton-electron scattering is the most important scattering mechanisms leading to the emission of the A-line. High purity p-type samples 7 with carrier concentration (NA --ND)between 6.6 x 1013 and 5 x 1014 cm -3 and hole mobilities between 9.7 x 103 and 8.2 x 10 a cm 2/Vsec were used in our experiments. The as-grown faces of the samples were excited by a superradiant, N2-1aser pumped dye laser (Rhodamin 6G) which was focussed with a small focal length lens ( f = 18 mm) and then imaged onto the sample. The excitation power density was varied in a range of about 3 - 3 0 0 kW/cm 2 . Magnetic fields up to flux densities of 10 T were.produced with a split coil superconducting magnet. Typical luminescence spectra are depicted in Fig. 1. In a semilogarithmic plot the emission intensity of the A-line is drawn vs photon energy for zero magnetic field and for a magnetic flux density of 9.9 T at an excitation power density of about 8 kW/cm:. Except for small zero field shifts of the position of the A-line and changes in emission intensity, the data do not depend on excitation power up to power
1186
MAGNETOLUMINESCENCE STUDIES IN HIGH PURITY GaAs WAVELENGTH
Vol. 17, No. 9
[~j
g200
8t50
i
r
P-
GaAs
(JZI/48)
T= 2K I • 8KW/cm 2
GaAs
~0S
dZ I / 4 8
0
~, 102
T=2K
A
4'
Z = S K W / c m ;~
! S
E
D
w
2
""".,,,
i
..........
,..'""
-2 I 2
J 4
I
6
I 8
110
MAGNETIC FLUX DENS!TY {TI z
FIG. 2. Energy shift of the emission line A and the (,4 o, X) bound exciton in magnetic fields. The broken line shows the shift of the free exciton emission. These data are taken from reference 6, The dotted line shows the energy shift one would expect for an emission line due to exciton-exciton scattering. I I 5~
i
_ _ ~ 52
PHOTCN
E~E~3~
e,
FIG. 1. Emission spectrum of sample JZ1/48 INA -~@:(77 K ) = 2.5 x I0 ~4 cm -3 ] #p ( 7 7 K ) = 8.7 x 1 0 3 cm /Vsec at 2 K for zero magnetic field and a magnetic flux density of 9.9 T. densities of about 300 kWi'cm 2 . At higher excitation intensities the emission coming from the electron-hole plasma dominates the spectra) The magnetoluminescence data of this emission line will be discussed in a separate paper) a The lineshape and the emission intensity of the A-line do not change appreciably with magnetic field, however, a magnetic field induced shift of the position of the emission maximum is observed. The sharp emission line close to the maximum of the A-line is due to the recombination of a exciton bound to a neutral acceptor (Si). 9 This bound exciton recombination (A °, X) is always the strongest emission line in these p-type samples at low pumping levels. At these intermediate excitation levels the emission of the A and of the (A °, X)-line might not necessarily come from the same regions of the crystal. 8 At magnetic flux densities of 9.9 T the (A °, X) and the A-line are well separated from each other and additionally the (.4 °, X)-bound exciton shows a complex splitting which has been studied in detail by White e t al. a°
Figure 2 shows the energy shift of the A-line with magnetic field. Additionally the energy shift of the center of gravity of the (,4 °, X)-emission line is depicted in Fig. 2, however this line will not be discussed in this paper. The broken line represents a curve drawn through the experimental data of Dreybrodt et a[. 6 obtained for the energy shift of the free exciton with magnetic field. It can be seen that the shift of the A-line is exactly the same as for the free exciton. Since for an exciton-electron scattering process, the energy of the emitted photon at zero magnetic fields is given by hw~_e, = f x + f~i,~,~, - A £ e z
(t)
where hw is the photon energy, E~. is the energy of the free exciton, Ekin, x its kinetic energy and AE~l the energy transferred to the scattered electron (at zero magnetic field /',Eel must be only kinetic energy of the electron), the magnetic field dependence of the A-line is mainly given by
h~x-ez(/-/) = fx(o) + AEx(H) +Ekin,~ -,~E~z (2) where A E : , ( H ) is the magnetic field induced energy shift of the free exciton. Combining equation (1) and (2) yields:
,ana)x, ez(H) = ,aExf~r)
(3)
which is in agreement with our results. The magnetic field induced energy shift for a recombination line
Vol. 17, No. 9
MAGNETOLUMINESCENCE STUDIES IN HIGH PURITY GaAs
due to exciton-exciton scattering is expected to be completely different. Assuming scattering of excitons into continuum states only, the high energy onset of an emission line due to exciton-exciton scattering is
given by hcomax, x-x = 2E~ -- E~
(at H = 0).
(4)
The magnetic field dependence will then be given by h ~ m ~ , ~ _ ~ ( n ) = 2Ex(0) + 2AE~(/4)--E,(0)
- ZxE, (H)
(5)
where AEg (H)is the shift of the lowest Landau level: Since the spin splitting is small compared to the Landau splitting, spin effects are neglected, AEe(H) = 1]2(e]lac)H OR is the reduced mass of the exciton). Assuming that the shift of the emission maximum will be the same as for the high energy onset one gets from equation (3) and (4): Ahcox_x(n) = 2AEx(H)--AEe(I'I).
(6)
This curve is also shown in Fig. 2 (dotted line). For AEx(H) again the data of reference 6 were taken. AEe(H ) was calculated with a reduced mass of/a = 0.595, which only takes into account the heavy, holes, but since we are interested only in a qualitative curve this is sufficient. The striking features of this curve are, that at small magnetic fields the shift of the emission maximum is to lower energies first, which is due to the increase of exciton binding energy. At high magnetic fields a linear shift of the maximum to higher energies is expected for an exciton-exciton scattering process. Since this curve does not fit our data, one has to assume that exciton-exciton scattering is not a very efficient recombination process for the free exciton, contrary to the results of I I - V I
1187
compounds. 12 However, this seems to be reasonable, since the exciton binding energy in most of the I I - V I compounds is large compared with the exciton binding energy of GaAs (4.2 meV 4) and henceforth the number of free electrons is expected to be much more smaller. Our results indicate that in case a sufficient number of electrons is present, exciton-electron scattering is the most efficient radiative recombination channel for the free exciton at high densities. It is also interesting to note that the result we obtained for the center of gravity shift of the (A °, X) line, are in good agreement with theoretical considerations, n It is expected that the magnetic field shift of the exciton bound to Si (binding energy comparable with free exciton energy) is slightly less than that for the free exciton, as observed in our experiments. In conclusion, the magnetoluminescence data of the A-line show that exciton-electron scattering as described by equation (3) is the dominant recombination mechanism for free excitons at high excitation levels. Exciton--exciton scattering, which seems to be important in semiconductors having large exciton binding energies like most of the I I - V I compounds, 12 while it might present, does not contribute appreciably to the recombination of free excitons in GaAs.
Acknowledgements - W e thank Dr. K.-H. Zschauer, Siemens, Forschungslabor Mimchen, for making available to us his high quality GaAs samples and Dr. D. Bimberg, Hochfeld-Magnetlabor, Grenoble, for carefully reading the manuscript. One of the authors (E.G.) gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft by means of a fellowship.
REFERENCES 1.
G(SBEL E., HERZOG H., PILKUHN M.H. & ZSCHAUER K.H., Solid State Commun. 13, 719 (1973).
2.
HILDEBRAND O. & G~3BEL E., Proc. 12th Int. Conf. Phys. Semicond., pp. 147. Teubner-Verlag, Stuttgart (1974).
3.
MORIYA T. & KUSHIDA T., Solid State Commun. 12,495 (1973).
4.
SELL D.D., DINGLE R., STOKOWSKI S.E. & DILORENZO J.V., Phys. Rev. Lett. 27, 1644 (1971).
5.
WHITE A.M., DEAN P.J., TAYLOR L.L., CLARKE R.C.; ASHEN D.J., MULLIN J.B. & GREENE P.D.,
J. Phys. 15, 1727 (1972). 6.
WILLMANN F., SUGA S., DREYBRODT W. & CHO V., Solid State Commun. 14,783 (1974); DREYBRODT W WlLLMANN F., BETTINI M. & BAUSER E., Solid State Commun. 12, 1217 (1973); see also: DINGLE R., Phys. Rev. B8, 4627 (1973).
1188
MAGNETOLUMINESCENCE STUDIES IN HIGH PURITY GaAs
Vol. 17, No. 9
7.
ZSCHAUER K.H., Proc. lnt. Syrup. on GaAs and Related Compounds, p. 3. Boulder, Colorado (1973).
8.
Gt3BEL E. & PILKUHN M.H., J. Phys. 35, C3-191 (1974).
9.
SHAHJ.,LEITER.C.C.&NAHORYR.E.,Phys. Rev. 184,811 (1969).
10.
WHITE A.M., DEAN P.J. & DAY B., J. Phys. C7, 1400 (1974).
11.
WlLLMANNF.,DREYBRODTW.&BETTINIM.,Phys. Rev. BS, 2891 (1973).
12.
See e.g. MADGE D. & MAHR H.,Phys. Rev. B2, 4098 (1970) and BENOIT A LA GUILLAUME C., DEBEVER J.M. & SALVAN F., Proc. Conf. Phys. Semicond. pp. 581. Moscow (1968).
13.
GOBEL E., SHAKLEE K.L., EPWORTH R. (to be published).
Pergamon Press.
Printed in Great Britain
MAGNETOLUMINESCENCE STUDIES OF EXCITONIC SCATTERING PROCESSES IN HIGH PURITY GaAs E. G6bel,* K.L. Shaklee and R. Epworth Bell Telephone Laboratories, Holmdel, NJ 07733, U.S.A.
(Received 18 June 1975 by A.G. Chynoweth)
The broad emission line at about 1.512 eV, which dominates the emission spectra of pure GaAs at intermediate excitation levels (1-300 kW/cm 2 ) and low temperatures (< 40 K) is investigated in magnetic fields up to magnetic flux densities of 10 T. The shift of the emission maximum in the magnetic field is exactly the same as recently reported for the free exciton. This demonstrates that at high excitation levels exciton-electron scattering is the dominant mechanism for the radiative decay of free excitons.
THE LUMINESCENCE spectra of pure GaAs at low temperatures change considerably at high pumping levels. One of the characteristic features of the "high intensity" luminescence is the occurrence of a broad emission line at about 1.52 eV (A-line) (the energetic position depends slightly on excitation power), which dominates the spectra at intermediate excitation levels ("- 1-300 kW/cm 2). Based on energetic arguments, 1' a, s lineshape fits s and on the results of the electric field,a doping s and temperature dependence, 1 as well as excitation spectroscopy results 2 this emission line is interpreted in terms of excitonic scattering processes. However, up to now no clear choice between excitonexciton or exciton-electron scattering as the dominant mechanism for the radiative decay of free excitons at these high excitation levels could be made. All other radiative recombination channels for the free exciton (i.e. direct recombination of the exciton-polariton 4 at 1.5157 eV and 1.5146 eV in our samples and the LO-phonon replica at about 1.479 eV 5) are less important at the excitation powers discussed in this paper as can be shown by a comparison of the integrated emission intensities. In this paper we report on magnetohiminescence *Permanent address: Physikalisches Institut, University of Stuttgart, DTO00 Stuttgart 80, Pfaffenwaldring 58, Fed. Rep. Germany. 1185
studies of the A-line in magnetic fields up to flux densities of 10 T. Additionally the experimental data are compared with recent magnetoluminescence results for the free exciton.6 This comparison clearly shows that exciton-electron scattering is the most important scattering mechanisms leading to the emission of the A-line. High purity p-type samples 7 with carrier concentration (NA --ND)between 6.6 x 1013 and 5 x 1014 cm -3 and hole mobilities between 9.7 x 103 and 8.2 x 10 a cm 2/Vsec were used in our experiments. The as-grown faces of the samples were excited by a superradiant, N2-1aser pumped dye laser (Rhodamin 6G) which was focussed with a small focal length lens ( f = 18 mm) and then imaged onto the sample. The excitation power density was varied in a range of about 3 - 3 0 0 kW/cm 2 . Magnetic fields up to flux densities of 10 T were.produced with a split coil superconducting magnet. Typical luminescence spectra are depicted in Fig. 1. In a semilogarithmic plot the emission intensity of the A-line is drawn vs photon energy for zero magnetic field and for a magnetic flux density of 9.9 T at an excitation power density of about 8 kW/cm:. Except for small zero field shifts of the position of the A-line and changes in emission intensity, the data do not depend on excitation power up to power
1186
MAGNETOLUMINESCENCE STUDIES IN HIGH PURITY GaAs WAVELENGTH
Vol. 17, No. 9
[~j
g200
8t50
i
r
P-
GaAs
(JZI/48)
T= 2K I • 8KW/cm 2
GaAs
~0S
dZ I / 4 8
0
~, 102
T=2K
A
4'
Z = S K W / c m ;~
! S
E
D
w
2
""".,,,
i
..........
,..'""
-2 I 2
J 4
I
6
I 8
110
MAGNETIC FLUX DENS!TY {TI z
FIG. 2. Energy shift of the emission line A and the (,4 o, X) bound exciton in magnetic fields. The broken line shows the shift of the free exciton emission. These data are taken from reference 6, The dotted line shows the energy shift one would expect for an emission line due to exciton-exciton scattering. I I 5~
i
_ _ ~ 52
PHOTCN
E~E~3~
e,
FIG. 1. Emission spectrum of sample JZ1/48 INA -~@:(77 K ) = 2.5 x I0 ~4 cm -3 ] #p ( 7 7 K ) = 8.7 x 1 0 3 cm /Vsec at 2 K for zero magnetic field and a magnetic flux density of 9.9 T. densities of about 300 kWi'cm 2 . At higher excitation intensities the emission coming from the electron-hole plasma dominates the spectra) The magnetoluminescence data of this emission line will be discussed in a separate paper) a The lineshape and the emission intensity of the A-line do not change appreciably with magnetic field, however, a magnetic field induced shift of the position of the emission maximum is observed. The sharp emission line close to the maximum of the A-line is due to the recombination of a exciton bound to a neutral acceptor (Si). 9 This bound exciton recombination (A °, X) is always the strongest emission line in these p-type samples at low pumping levels. At these intermediate excitation levels the emission of the A and of the (A °, X)-line might not necessarily come from the same regions of the crystal. 8 At magnetic flux densities of 9.9 T the (A °, X) and the A-line are well separated from each other and additionally the (.4 °, X)-bound exciton shows a complex splitting which has been studied in detail by White e t al. a°
Figure 2 shows the energy shift of the A-line with magnetic field. Additionally the energy shift of the center of gravity of the (,4 °, X)-emission line is depicted in Fig. 2, however this line will not be discussed in this paper. The broken line represents a curve drawn through the experimental data of Dreybrodt et a[. 6 obtained for the energy shift of the free exciton with magnetic field. It can be seen that the shift of the A-line is exactly the same as for the free exciton. Since for an exciton-electron scattering process, the energy of the emitted photon at zero magnetic fields is given by hw~_e, = f x + f~i,~,~, - A £ e z
(t)
where hw is the photon energy, E~. is the energy of the free exciton, Ekin, x its kinetic energy and AE~l the energy transferred to the scattered electron (at zero magnetic field /',Eel must be only kinetic energy of the electron), the magnetic field dependence of the A-line is mainly given by
h~x-ez(/-/) = fx(o) + AEx(H) +Ekin,~ -,~E~z (2) where A E : , ( H ) is the magnetic field induced energy shift of the free exciton. Combining equation (1) and (2) yields:
,ana)x, ez(H) = ,aExf~r)
(3)
which is in agreement with our results. The magnetic field induced energy shift for a recombination line
Vol. 17, No. 9
MAGNETOLUMINESCENCE STUDIES IN HIGH PURITY GaAs
due to exciton-exciton scattering is expected to be completely different. Assuming scattering of excitons into continuum states only, the high energy onset of an emission line due to exciton-exciton scattering is
given by hcomax, x-x = 2E~ -- E~
(at H = 0).
(4)
The magnetic field dependence will then be given by h ~ m ~ , ~ _ ~ ( n ) = 2Ex(0) + 2AE~(/4)--E,(0)
- ZxE, (H)
(5)
where AEg (H)is the shift of the lowest Landau level: Since the spin splitting is small compared to the Landau splitting, spin effects are neglected, AEe(H) = 1]2(e]lac)H OR is the reduced mass of the exciton). Assuming that the shift of the emission maximum will be the same as for the high energy onset one gets from equation (3) and (4): Ahcox_x(n) = 2AEx(H)--AEe(I'I).
(6)
This curve is also shown in Fig. 2 (dotted line). For AEx(H) again the data of reference 6 were taken. AEe(H ) was calculated with a reduced mass of/a = 0.595, which only takes into account the heavy, holes, but since we are interested only in a qualitative curve this is sufficient. The striking features of this curve are, that at small magnetic fields the shift of the emission maximum is to lower energies first, which is due to the increase of exciton binding energy. At high magnetic fields a linear shift of the maximum to higher energies is expected for an exciton-exciton scattering process. Since this curve does not fit our data, one has to assume that exciton-exciton scattering is not a very efficient recombination process for the free exciton, contrary to the results of I I - V I
1187
compounds. 12 However, this seems to be reasonable, since the exciton binding energy in most of the I I - V I compounds is large compared with the exciton binding energy of GaAs (4.2 meV 4) and henceforth the number of free electrons is expected to be much more smaller. Our results indicate that in case a sufficient number of electrons is present, exciton-electron scattering is the most efficient radiative recombination channel for the free exciton at high densities. It is also interesting to note that the result we obtained for the center of gravity shift of the (A °, X) line, are in good agreement with theoretical considerations, n It is expected that the magnetic field shift of the exciton bound to Si (binding energy comparable with free exciton energy) is slightly less than that for the free exciton, as observed in our experiments. In conclusion, the magnetoluminescence data of the A-line show that exciton-electron scattering as described by equation (3) is the dominant recombination mechanism for free excitons at high excitation levels. Exciton--exciton scattering, which seems to be important in semiconductors having large exciton binding energies like most of the I I - V I compounds, 12 while it might present, does not contribute appreciably to the recombination of free excitons in GaAs.
Acknowledgements - W e thank Dr. K.-H. Zschauer, Siemens, Forschungslabor Mimchen, for making available to us his high quality GaAs samples and Dr. D. Bimberg, Hochfeld-Magnetlabor, Grenoble, for carefully reading the manuscript. One of the authors (E.G.) gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft by means of a fellowship.
REFERENCES 1.
G(SBEL E., HERZOG H., PILKUHN M.H. & ZSCHAUER K.H., Solid State Commun. 13, 719 (1973).
2.
HILDEBRAND O. & G~3BEL E., Proc. 12th Int. Conf. Phys. Semicond., pp. 147. Teubner-Verlag, Stuttgart (1974).
3.
MORIYA T. & KUSHIDA T., Solid State Commun. 12,495 (1973).
4.
SELL D.D., DINGLE R., STOKOWSKI S.E. & DILORENZO J.V., Phys. Rev. Lett. 27, 1644 (1971).
5.
WHITE A.M., DEAN P.J., TAYLOR L.L., CLARKE R.C.; ASHEN D.J., MULLIN J.B. & GREENE P.D.,
J. Phys. 15, 1727 (1972). 6.
WILLMANN F., SUGA S., DREYBRODT W. & CHO V., Solid State Commun. 14,783 (1974); DREYBRODT W WlLLMANN F., BETTINI M. & BAUSER E., Solid State Commun. 12, 1217 (1973); see also: DINGLE R., Phys. Rev. B8, 4627 (1973).
1188
MAGNETOLUMINESCENCE STUDIES IN HIGH PURITY GaAs
Vol. 17, No. 9
7.
ZSCHAUER K.H., Proc. lnt. Syrup. on GaAs and Related Compounds, p. 3. Boulder, Colorado (1973).
8.
Gt3BEL E. & PILKUHN M.H., J. Phys. 35, C3-191 (1974).
9.
SHAHJ.,LEITER.C.C.&NAHORYR.E.,Phys. Rev. 184,811 (1969).
10.
WHITE A.M., DEAN P.J. & DAY B., J. Phys. C7, 1400 (1974).
11.
WlLLMANNF.,DREYBRODTW.&BETTINIM.,Phys. Rev. BS, 2891 (1973).
12.
See e.g. MADGE D. & MAHR H.,Phys. Rev. B2, 4098 (1970) and BENOIT A LA GUILLAUME C., DEBEVER J.M. & SALVAN F., Proc. Conf. Phys. Semicond. pp. 581. Moscow (1968).
13.
GOBEL E., SHAKLEE K.L., EPWORTH R. (to be published).