- Email: [email protected]
Picosecond decay kinetics of CdS luminescence studied by a streak camera
Solid State Communications, Vol. 31, pp. 253—256. Pergamon Press Ltd. 1979. Printed in Great Britain. PICOSECOND DECAY KINETICS OF CdS LUMINESCENCE STUDIED BY A STREAK CAMERA T. Kobayashi,* Y. Segawa and S. Namba The Institute of Physical and Chemical Research, Wako, Saitama, Japan
(Received 12 March 1979 by Y. Toyozawa) Using a picosecond laser and a streak camera we have observed the time dependence of the luminescence intensity of free excitons, bound excitons, and excitonic molecules in CdS. The observed kinetics show that the P band is due to bimolecular emission from free excitons and that bound excitons are generated from free excitons through monomolecular process and excitonic molecule through bimolecular process.
AT HIGH density excitation of Il—Vt semiconductors such as CdS, new interaction channels between excitons open up, notably coffision quenching between excitons and formation of exciton complexes. The luminescence spectrum of CdS crystal observed at various excitation intensities shows emission bands at 486.9,487.3,490.5, and 492.5 nm; these bands are attributed to exciton bound to neutral donors (12 band), excitonic molecule (M band), inelastic exciton—exciton scattering (P band), and free exciton luminescence accompanied by LO phonon emission (A—LO band), respectively. Because of the short time constants of the luminescence decay processes, the decay kinetics of the luminescence have been very rarely studied with a few exceptions [1—3]. A method which uses a Kerr cell shutter has been applied to a study of CdS and CdSe luminescences. The interpre. tation of the spectra obtained is complicated because of induced emission [2]. Using an up-conversion light gate, Daly and Mahr have obtained data which are indicative of the formation of electron—hole liquid [3]. Streak cameras have been used generally for laser diagnostics [3] and more recently with bandpass filters [4] for the luminescence studies. We have used a streak camera and picosecond excitation to study CdS luminescence. We excite CdS with a mode-locked ruby laser. The peak power, total energy, and pulse width of the amplified single pulse from the mode-locked ruby laser presently used are 3—10 GW, 60—200 mJ, and 20 psec, respectively. The second barmonic of the ruby laser has 20 psec pulse width, 0.3—1 GW peak power, and 6—10 mJ energy. Spectral resolution of the 50 cm grating monochromator used in the second order is about ±0.3 nm. The image of the exit slit is focused onto the photocathode of an image *
converter streak camera (IMACON 600) coupled with the three stage image intensifier (EM! 9914), the intensified silicon intensified target tube (ISIT, PAR 1205!), optical multichannel analyzer (OMA, PAR 1205A), and a desk top computer (HP 9825 A). Detail of the experimental equipment will be given elsewhere [5]. The crystalline sample was grown from the vapor phase into a thin crystal (5 x 5 x 0.1 mm3 in size). We used four different crystalline samples and all of them gave the same constants within experimental errors. The spectrum of a sample excited by an Hg lamp consists of one main luminescence band at 486.9 nm which is designated as the radiative decay of a bound exciton (12). Under the laser excitation at ~ 1 x 106 W cm2 new emission bands appear at 490.5 rim (P), 4873 nm (M) and 492.5 nm (A—LO). The emission spectrum at 1—2 x 106 W cm2 is shown in Fig. 1 together with that obtained by Hg excitation. When the peak power of the excitation pulse is increased to 3—5 x 1 o~W cm2 the spectrum is changed from that of low density laser excitation. The relative intensity of A—LO and P band are all higher than that of 12. Other than these bands, the most obviousfeature ofthe spectrum at high density excitation (3—5 x 107W cm2) is the ,
,
appearance ofa new broad band whose peak wavelength is around 496 nm. In the excitation peak power range 1_S x 106 W cm2 where the bmad band does not appear or is very weak, the emission intensity of M and
P bands is nearly quadratic to the excitation laser intensity, while that of 12 bound exciton band is nearly linear to the excitation intensity. At excitation densities higher than 5 x i07 W cm2 the P band has a very large gain and stimulated emission occurs readily. Accordingly as the excitation light intensity increases, stimulated emission occurs and theP band grows superlinearly, Present address: Bell Laboratories Murray Hill NJ while the 12 bound exciton band disappears. In order to 07974, U.S.A. On leave temporarily from the Institute avoid the effect of stimulated emission we used a laser of Physical and Chemical Research. intensity where it is assured that the stimulated emission does not take place. 253
254
PICOSECOND DECAY KINETICS OF CdS LUMINESCENCE 2 CdS/4.2K
Vol. 31, No.4
A-L0
LASER EXCITATION
—
j S LL_
‘
I 486
I
I 488
i
I 490
i
I
i
492
I
494
i
I
496
~
498
WAVELENGTH (nm) Fig. 1. Emission spectrum of CdS excited by 100 W high pressure Hg lamp with Hoya filter B-36 (365 urn Hg line) The spectrum of CdS excited by the second harmonic of ruby laser at the excitation density of 1—2 x 106 W cm 2~ (-). ~
We used four CdS crystals of different size. The geometry of excitation and detection of emission was changed. The emission spectra observed for the four different CdS crystals with different geometries of excitation and detection were quite similar at the same excitation power. We could not see any difference in the spectra when the excitation and observation geometry was changed. The decay curves of the A—LO and P bands observed when the excitation density is about 3—6 x 106 W cm2, are shown in Fig. 2. The A—LO line which decays nearly exponentially has a measured decay time constant of 145 ±5 psec. When the excitation intensity is increased to 1.5—3 x iO~W cm2, the decay of A—LO line is again close to exponential decay and the time constant is 128 ±19 psec. The rise of the A—LO band luminescence was found to follow the convolution of the excitation laser pulse shape, the luminescence decay curve and the time resolution function of the detection system. Therefore the rise time constant of the A—LO luminescence is considerably shorter than the resolution of the equipment used in the present study, 40 psec. The luminescence intensity of the P band observed at 490.5 nm also shows an exponential decay, and the time constant of the decay luminescence is 77 ±2 psec at3—6x 106 Wcm2 and 69±4psecat1.5—3 x 107W cm2. The rise time of the luminescence intensity was also found to be shorter than 40 psec.
The luminescence intensity of the excitonic molecule (M) at the excitation density of 3—6 x 106 W cm2 is shown in Fig. 2. The luminescence intensity decays exponentially with a time constant of 225 ±62 psec. The time constant of the decay at an excitation density of 1.5—3 x l0~W cm2 becomes shorter (173 ±12 psec). It is found that the luminescence intensity from M has a slower rise than the convolution curve of the laser pulse shape, decay curve of luminescence, and resolution function of the equipment. The rise time was obtained by the subtraction of the rising part of the luminescence intensity from the extrapolated line obtained from the decaying part. This gives a linear plot as is shown in Fig. 2. From the slope of this line, a rise time constant of 71 ±9 psec was obtained for the excitation density of 3—6 x 106 W cm2. The rise time constant at an excitation density of 1 .5—3 x iO~W cnf2 was 65 ±8 psec. The 12 bound exciton at 486.9 nm has a very long lifetime of about 3—4 nsec at both 3—6 x 106 W cm2 and 1.5—3 x iO~W cm2. The rise time was estimated to be 150 ±90 psec at 3—6 x iO~W cm2 and it was 130 ±70 psec at 1.5—3 x iO~W cm2. We have observed the time dependence ofluminesc. ence intensity at other wavelengths than 486.9,487.3, 490.5, and 492.5 nm at excitation densities of both 3—6x l0~Wcm2 and 1.5—3x 108 Wcm2.The wavelengths we observed the luminescence were 487.2, 487.5,491.0,491.2 and 497.5. The decay and rise
Vol.31, No.4
PICOSECOND DECAY KINETICS OF CdS LUMINESCENCE
255
io3~ 0 cds 4.2K 0 0
A-LO 492.5nm
,~ 0
>
2
~1O-
. •
0
P 490.Snm
0 0 0 0
4
z
w 0 W
0
10~
M
~
o
0
o
0
‘ce 487.3nm
c%O ~
100
200
300 TIME
400
500
600
700
(psec)
FIg. 2. Asemllogarithmlc plot of the luminescence ‘intensity vs time after a picosecond pulse excitation of CdS at4.2 K. Wavelength of the monochromator was adjusted to 492.5 mn to observe A—LO line (open circle, line 1), 490.5 nm to observe P line (closed circle, line 2), and 487.3 mu to observe M line (open square, line 3). kineticsof49l.Oand49l.2nmattheexcitationdensity of 3—6 x 106 W cm2 were similar to those of 490.5 rim at the same excitation density. The decay and rise kine-
3—6x 106 Wcm2 and 1.5—3 x l0~Wcm2.Atthe wavelength of 487.5 nm, the decay curve of the luminescence intensity is clearly composed of two compo-
tics at 487.2 urn is very close to that at 4873 urn at
nents of long and short lifetimes. The lifetime of short
256
PICOSECOND DECAY KINETICS OF CdS LUMINESCENCE
component is nearly equal to that at 487.3 and 487.2 mu, while the long lifetime is close to that at 486.9 mu. Therefore, at 497.5 mu, the luminescence has two components corresponding to 12 bound exciton and M. From these experimental results we can discuss the mechanism of the formation and decay processes of various excited species, namely electron-hole pairs, free excitons, 12 bound excitons, and excitonic molecules. After laser excitation, electron—hole pairs are generated at the initial stage of excitation and then they are converted to free excitons. The P band has been attributed to be emission from free excitons by bimolecular process and A—LO band by monomolecular process. Excitonic molecules and bound excitons have been thought to be formed by biexcitonic combination and monoexcitonic trapping of free excitons, respectively, From the above mechanism and with the assumption that only one kind of bound excitons exists, the rate equations are as follows, dflf.ex/dt dflbex/dt
=
—
=
anf.ex
~f.ex —
—
+ 6,,~
~
dflmoi/dt = (3~~f.ex 6~mol where ~ ~ and ~mot are the number of the free excitons, bound excitons, and the excitonic molecules, respectively. The monomolecular and bimolecular decay rate constants of free exciton are represented by a and ~3,respectively. The formation time constants of bound excitons and excitonic molecule are represented by a’ and j3’, respectively. The decay rate constants ofbound excitons and excitonic molecules are represented by 7 and 6, respectively.! is the intensity of the exciting laser pulse which has a pulse width of 20 psec and a is the absorption cross-section of CdS at 357 mu. Since free excitons emit A—LO luminescence by a monomolecular process and P luminescence by a bi. molecular process, the time dependence of the A—LO —
luminescence intensity follows that of the free exciton concentration n,.~(t)and that of the P luminescence intensity follows that of n~(t). Since excitonic molecules (M) and bound excitons (B.E.) are generated from free excitons by bimolecular and monomoleuclar processes, respectively, the formation rates of M and B.E. are proportional to n~~(t) and fl~,~(t),respectively. From the experimental results, the decay curves of A—LO, P. and molecule luminescences are exponential. This means either that the transition probabifity of A—LO luminescence emission is much higher than that of bimolecular P luminescence or that the monomolecular capture cross-section of a free exciton to form a
Vol.31, No.4
bound exciton is much larger than that of the bimolecular capture cross-section of a free exciton to form an excitonic molecule. All of the luminescence from free excitons, excitonic molecules, and bound excitons show quasi. exponential rise and decay. The decay and rise times of the luminescence are not expected to be constant but change with time when the mechanism of the luminescence is taken into account. Since the time constant of the quasi-exponential decay of the A—LO was ohserved to be 145 psec at 3—6 x 106 W cm2 and 128 psec at 1.5—3 x I o~ W cm2 the decay time of P line and the rise time of M band should be half of it, i.e. 72.5 psec at 3—6 x 106 W cnf2 and 64 psec at 1.5—3 x 1 o~ W cm2, and the rise time of the bound exciton should be 145 psec. The observed decay time constant for P band is 77 psec at 3—6 x 106 W cm2 and 69 psec at 1.5—3 x iO~W cm2, the observed rise time constant for M is 71 psec at 3—6 x io~ W cm2 and 65 psec at 1.5—3 x iO~W cm2. The rise time constant observed for ‘2 bound exciton is 150 psec at 3—6 x 10~W cm’2 and 130 psec at 1.5—3 x iO~W cm2. These values are consistent with the decay time constant of the A—LO band. This provides direct support for this mechanism for the formation process of bound excitons and excitonic molecules and also the mechanism of the P band luminescence. ,
Acknowledgements The authors want to express their sincere gratitude to S. Nagakura for his continuing interest and encouragement during the work. They also wish to thank D. H. Auston for critical reading. —
REFERENCES 1.
2.
3. 4,
5. 6.
D. von der Linde, (Jitrashort Light Pulses. Picosecond Techniques and Applications (Edited by S.L. Shapiro), pp. 203 —273. Springer-Verlag, references therein. H. Kuroda & S. Shionoya,J. Phys. Soc. Japan 36, 476 (1974); M. Hayashi, H. Saito & S. Shionoya, Solid State Commun. 24, 837 (1977). M. Ojima, T. Kushida, Y. Tanaka & S. Shionoya, Solid State Commun. 24, 841 (1977). T. Daly & H. Mahr, Solid State Commun. 25,323 (1978). D.J. Bradley, Ultrashort LightPulses. Picosecond Techniques and Applications, pp. 16—78 (Edited by Shapiro). Sp~igerVerlag, Berlin, andS.L. references therein. T. Kobayashi, J. Phys. Chem. 82,2277 (1978). E.G. Arthurs, DJ. Bradley & A.G. Roddie, Chem. Phys. Lett. 22, 230 (1973). Opt. Commun. 8, 118 (1973).
(Received 12 March 1979 by Y. Toyozawa) Using a picosecond laser and a streak camera we have observed the time dependence of the luminescence intensity of free excitons, bound excitons, and excitonic molecules in CdS. The observed kinetics show that the P band is due to bimolecular emission from free excitons and that bound excitons are generated from free excitons through monomolecular process and excitonic molecule through bimolecular process.
AT HIGH density excitation of Il—Vt semiconductors such as CdS, new interaction channels between excitons open up, notably coffision quenching between excitons and formation of exciton complexes. The luminescence spectrum of CdS crystal observed at various excitation intensities shows emission bands at 486.9,487.3,490.5, and 492.5 nm; these bands are attributed to exciton bound to neutral donors (12 band), excitonic molecule (M band), inelastic exciton—exciton scattering (P band), and free exciton luminescence accompanied by LO phonon emission (A—LO band), respectively. Because of the short time constants of the luminescence decay processes, the decay kinetics of the luminescence have been very rarely studied with a few exceptions [1—3]. A method which uses a Kerr cell shutter has been applied to a study of CdS and CdSe luminescences. The interpre. tation of the spectra obtained is complicated because of induced emission [2]. Using an up-conversion light gate, Daly and Mahr have obtained data which are indicative of the formation of electron—hole liquid [3]. Streak cameras have been used generally for laser diagnostics [3] and more recently with bandpass filters [4] for the luminescence studies. We have used a streak camera and picosecond excitation to study CdS luminescence. We excite CdS with a mode-locked ruby laser. The peak power, total energy, and pulse width of the amplified single pulse from the mode-locked ruby laser presently used are 3—10 GW, 60—200 mJ, and 20 psec, respectively. The second barmonic of the ruby laser has 20 psec pulse width, 0.3—1 GW peak power, and 6—10 mJ energy. Spectral resolution of the 50 cm grating monochromator used in the second order is about ±0.3 nm. The image of the exit slit is focused onto the photocathode of an image *
converter streak camera (IMACON 600) coupled with the three stage image intensifier (EM! 9914), the intensified silicon intensified target tube (ISIT, PAR 1205!), optical multichannel analyzer (OMA, PAR 1205A), and a desk top computer (HP 9825 A). Detail of the experimental equipment will be given elsewhere [5]. The crystalline sample was grown from the vapor phase into a thin crystal (5 x 5 x 0.1 mm3 in size). We used four different crystalline samples and all of them gave the same constants within experimental errors. The spectrum of a sample excited by an Hg lamp consists of one main luminescence band at 486.9 nm which is designated as the radiative decay of a bound exciton (12). Under the laser excitation at ~ 1 x 106 W cm2 new emission bands appear at 490.5 rim (P), 4873 nm (M) and 492.5 nm (A—LO). The emission spectrum at 1—2 x 106 W cm2 is shown in Fig. 1 together with that obtained by Hg excitation. When the peak power of the excitation pulse is increased to 3—5 x 1 o~W cm2 the spectrum is changed from that of low density laser excitation. The relative intensity of A—LO and P band are all higher than that of 12. Other than these bands, the most obviousfeature ofthe spectrum at high density excitation (3—5 x 107W cm2) is the ,
,
appearance ofa new broad band whose peak wavelength is around 496 nm. In the excitation peak power range 1_S x 106 W cm2 where the bmad band does not appear or is very weak, the emission intensity of M and
P bands is nearly quadratic to the excitation laser intensity, while that of 12 bound exciton band is nearly linear to the excitation intensity. At excitation densities higher than 5 x i07 W cm2 the P band has a very large gain and stimulated emission occurs readily. Accordingly as the excitation light intensity increases, stimulated emission occurs and theP band grows superlinearly, Present address: Bell Laboratories Murray Hill NJ while the 12 bound exciton band disappears. In order to 07974, U.S.A. On leave temporarily from the Institute avoid the effect of stimulated emission we used a laser of Physical and Chemical Research. intensity where it is assured that the stimulated emission does not take place. 253
254
PICOSECOND DECAY KINETICS OF CdS LUMINESCENCE 2 CdS/4.2K
Vol. 31, No.4
A-L0
LASER EXCITATION
—
j S LL_
‘
I 486
I
I 488
i
I 490
i
I
i
492
I
494
i
I
496
~
498
WAVELENGTH (nm) Fig. 1. Emission spectrum of CdS excited by 100 W high pressure Hg lamp with Hoya filter B-36 (365 urn Hg line) The spectrum of CdS excited by the second harmonic of ruby laser at the excitation density of 1—2 x 106 W cm 2~ (-). ~
We used four CdS crystals of different size. The geometry of excitation and detection of emission was changed. The emission spectra observed for the four different CdS crystals with different geometries of excitation and detection were quite similar at the same excitation power. We could not see any difference in the spectra when the excitation and observation geometry was changed. The decay curves of the A—LO and P bands observed when the excitation density is about 3—6 x 106 W cm2, are shown in Fig. 2. The A—LO line which decays nearly exponentially has a measured decay time constant of 145 ±5 psec. When the excitation intensity is increased to 1.5—3 x iO~W cm2, the decay of A—LO line is again close to exponential decay and the time constant is 128 ±19 psec. The rise of the A—LO band luminescence was found to follow the convolution of the excitation laser pulse shape, the luminescence decay curve and the time resolution function of the detection system. Therefore the rise time constant of the A—LO luminescence is considerably shorter than the resolution of the equipment used in the present study, 40 psec. The luminescence intensity of the P band observed at 490.5 nm also shows an exponential decay, and the time constant of the decay luminescence is 77 ±2 psec at3—6x 106 Wcm2 and 69±4psecat1.5—3 x 107W cm2. The rise time of the luminescence intensity was also found to be shorter than 40 psec.
The luminescence intensity of the excitonic molecule (M) at the excitation density of 3—6 x 106 W cm2 is shown in Fig. 2. The luminescence intensity decays exponentially with a time constant of 225 ±62 psec. The time constant of the decay at an excitation density of 1.5—3 x l0~W cm2 becomes shorter (173 ±12 psec). It is found that the luminescence intensity from M has a slower rise than the convolution curve of the laser pulse shape, decay curve of luminescence, and resolution function of the equipment. The rise time was obtained by the subtraction of the rising part of the luminescence intensity from the extrapolated line obtained from the decaying part. This gives a linear plot as is shown in Fig. 2. From the slope of this line, a rise time constant of 71 ±9 psec was obtained for the excitation density of 3—6 x 106 W cm2. The rise time constant at an excitation density of 1 .5—3 x iO~W cnf2 was 65 ±8 psec. The 12 bound exciton at 486.9 nm has a very long lifetime of about 3—4 nsec at both 3—6 x 106 W cm2 and 1.5—3 x iO~W cm2. The rise time was estimated to be 150 ±90 psec at 3—6 x iO~W cm2 and it was 130 ±70 psec at 1.5—3 x iO~W cm2. We have observed the time dependence ofluminesc. ence intensity at other wavelengths than 486.9,487.3, 490.5, and 492.5 nm at excitation densities of both 3—6x l0~Wcm2 and 1.5—3x 108 Wcm2.The wavelengths we observed the luminescence were 487.2, 487.5,491.0,491.2 and 497.5. The decay and rise
Vol.31, No.4
PICOSECOND DECAY KINETICS OF CdS LUMINESCENCE
255
io3~ 0 cds 4.2K 0 0
A-LO 492.5nm
,~ 0
>
2
~1O-
. •
0
P 490.Snm
0 0 0 0
4
z
w 0 W
0
10~
M
~
o
0
o
0
‘ce 487.3nm
c%O ~
100
200
300 TIME
400
500
600
700
(psec)
FIg. 2. Asemllogarithmlc plot of the luminescence ‘intensity vs time after a picosecond pulse excitation of CdS at4.2 K. Wavelength of the monochromator was adjusted to 492.5 mn to observe A—LO line (open circle, line 1), 490.5 nm to observe P line (closed circle, line 2), and 487.3 mu to observe M line (open square, line 3). kineticsof49l.Oand49l.2nmattheexcitationdensity of 3—6 x 106 W cm2 were similar to those of 490.5 rim at the same excitation density. The decay and rise kine-
3—6x 106 Wcm2 and 1.5—3 x l0~Wcm2.Atthe wavelength of 487.5 nm, the decay curve of the luminescence intensity is clearly composed of two compo-
tics at 487.2 urn is very close to that at 4873 urn at
nents of long and short lifetimes. The lifetime of short
256
PICOSECOND DECAY KINETICS OF CdS LUMINESCENCE
component is nearly equal to that at 487.3 and 487.2 mu, while the long lifetime is close to that at 486.9 mu. Therefore, at 497.5 mu, the luminescence has two components corresponding to 12 bound exciton and M. From these experimental results we can discuss the mechanism of the formation and decay processes of various excited species, namely electron-hole pairs, free excitons, 12 bound excitons, and excitonic molecules. After laser excitation, electron—hole pairs are generated at the initial stage of excitation and then they are converted to free excitons. The P band has been attributed to be emission from free excitons by bimolecular process and A—LO band by monomolecular process. Excitonic molecules and bound excitons have been thought to be formed by biexcitonic combination and monoexcitonic trapping of free excitons, respectively, From the above mechanism and with the assumption that only one kind of bound excitons exists, the rate equations are as follows, dflf.ex/dt dflbex/dt
=
—
=
anf.ex
~f.ex —
—
+ 6,,~
~
dflmoi/dt = (3~~f.ex 6~mol where ~ ~ and ~mot are the number of the free excitons, bound excitons, and the excitonic molecules, respectively. The monomolecular and bimolecular decay rate constants of free exciton are represented by a and ~3,respectively. The formation time constants of bound excitons and excitonic molecule are represented by a’ and j3’, respectively. The decay rate constants ofbound excitons and excitonic molecules are represented by 7 and 6, respectively.! is the intensity of the exciting laser pulse which has a pulse width of 20 psec and a is the absorption cross-section of CdS at 357 mu. Since free excitons emit A—LO luminescence by a monomolecular process and P luminescence by a bi. molecular process, the time dependence of the A—LO —
luminescence intensity follows that of the free exciton concentration n,.~(t)and that of the P luminescence intensity follows that of n~(t). Since excitonic molecules (M) and bound excitons (B.E.) are generated from free excitons by bimolecular and monomoleuclar processes, respectively, the formation rates of M and B.E. are proportional to n~~(t) and fl~,~(t),respectively. From the experimental results, the decay curves of A—LO, P. and molecule luminescences are exponential. This means either that the transition probabifity of A—LO luminescence emission is much higher than that of bimolecular P luminescence or that the monomolecular capture cross-section of a free exciton to form a
Vol.31, No.4
bound exciton is much larger than that of the bimolecular capture cross-section of a free exciton to form an excitonic molecule. All of the luminescence from free excitons, excitonic molecules, and bound excitons show quasi. exponential rise and decay. The decay and rise times of the luminescence are not expected to be constant but change with time when the mechanism of the luminescence is taken into account. Since the time constant of the quasi-exponential decay of the A—LO was ohserved to be 145 psec at 3—6 x 106 W cm2 and 128 psec at 1.5—3 x I o~ W cm2 the decay time of P line and the rise time of M band should be half of it, i.e. 72.5 psec at 3—6 x 106 W cnf2 and 64 psec at 1.5—3 x 1 o~ W cm2, and the rise time of the bound exciton should be 145 psec. The observed decay time constant for P band is 77 psec at 3—6 x 106 W cm2 and 69 psec at 1.5—3 x iO~W cm2, the observed rise time constant for M is 71 psec at 3—6 x io~ W cm2 and 65 psec at 1.5—3 x iO~W cm2. The rise time constant observed for ‘2 bound exciton is 150 psec at 3—6 x 10~W cm’2 and 130 psec at 1.5—3 x iO~W cm2. These values are consistent with the decay time constant of the A—LO band. This provides direct support for this mechanism for the formation process of bound excitons and excitonic molecules and also the mechanism of the P band luminescence. ,
Acknowledgements The authors want to express their sincere gratitude to S. Nagakura for his continuing interest and encouragement during the work. They also wish to thank D. H. Auston for critical reading. —
REFERENCES 1.
2.
3. 4,
5. 6.
D. von der Linde, (Jitrashort Light Pulses. Picosecond Techniques and Applications (Edited by S.L. Shapiro), pp. 203 —273. Springer-Verlag, references therein. H. Kuroda & S. Shionoya,J. Phys. Soc. Japan 36, 476 (1974); M. Hayashi, H. Saito & S. Shionoya, Solid State Commun. 24, 837 (1977). M. Ojima, T. Kushida, Y. Tanaka & S. Shionoya, Solid State Commun. 24, 841 (1977). T. Daly & H. Mahr, Solid State Commun. 25,323 (1978). D.J. Bradley, Ultrashort LightPulses. Picosecond Techniques and Applications, pp. 16—78 (Edited by Shapiro). Sp~igerVerlag, Berlin, andS.L. references therein. T. Kobayashi, J. Phys. Chem. 82,2277 (1978). E.G. Arthurs, DJ. Bradley & A.G. Roddie, Chem. Phys. Lett. 22, 230 (1973). Opt. Commun. 8, 118 (1973).