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Superluminescence and brightening of gallium arsenide under interband absorption of picosecond light pulses
~
Solld State Communications, Vol. 72, No. 7, pp. 625-629, Printed in Great Britain.
1989.
0038-1098/8953.00+.00 Pergamon Press plc
S U F E R ~ I N E ~ C E AND BRIGHT~ING OF GALLIUMARSENIDEUNDER I N T ~ ABSORPTIONOF PICOSECONDLIGHT 1 ~ N.N.Ageeva, I.L.Bronevoi, E.G.Dyadyushkin and V.A.Mironov Institute of Radio Engineering and Electronics, USSR Academy of Sciences, USSR, t 0 ~ 0 7 , loscow, GSP- 3, Marx Avenue, t8 S.E.Ktmekov and V.I.Perel' A.F.Ioffe Physicotechn.lcal Institute, USSR Academy of Sciences,
U~R, i94021, Lenlngraae, yoAitekhnlcheskaya St., 28 (Received iO August 1289 by A.L.Efros)
The brigh_tening of the GaAs layer caused by picosecond light ~ulses ~ s been.studied, The .brigtening spectru= just attar exitation aces n.ot depena on the energy of. the exiting pulse t i f it exceems a certain thresnoldTana on the energy l~exof the exiting photons, either. This spectrum i s completely describable under the a s s u ~ t i o n , that the photoexcited.eleosrons and holes have the e e r ~ dystriDu~ion at the Aattice temperature (295K)and with the Farmy quasilevels ~ e and ~h s a t i s i:ying the condition ~., .-~h-Eg..This ~ l o w s to conc.lude, that carrier concent~ration is limitem Dy the recombination superluminescence. •~ne oDser~.ation.of the edge emission that correlated with the exciting puAse of' picosecund duration confirms this conoAuslon.
I. Approximately reversible brightening of a gallium arsenide layer under excitation by high-power picosecond light pulses with a photon energy ~ e x slightly exceeding the energy gap E width has been observed by I.Bronevoi et al I . During the pulse, the brightening is the higher, the greater is the exciting energy. Inluediately after the excitation pulse a residual brightening in a wide spectrum band is observed, this including transitions between the split off valence and conduction bands. The complete spectrum was independent of the exciting pulse energy, if this energy was above a certain tresh-_ old value. These results are explained ~ under the assumption that during almost the entire high-power pulse saturation was present, this meaning that Fermi quasi-levels of electrons and holes meet the condition ~e- ~ h = ~ e x ' which correspond to complete brightening of the layer for the exciting light. Another possible cause of revereible brightening (also mentioned in2) is related to recombination induced by superluminesoenoe. Even before saturation is established, at We- ~ > E , in the spectral band
E < ~ < Pe- ~ population inversion occurs which can result in superluminesoenoe. Under such conditions each spontaneous emission photon induces recombination of a large number (of the order of exp(ka), where "k" is the enhancement factor and "a" is the diameter of the light spot) of electron-hole pairs. The effective recombination time may be rather short. Experimental results I did not allow to distinguish between condition ~e- ~ = ~ e x (saturati°n) and ~e- ~ = E (complete control by superluminesoenoe), since in these experiments I the difference ~ e x - E g was less than the thermal energy of carriers kT. The significant role of recombination superluminescence is strongly confirmed by anomalous emission of excited GaAs layers 3 of a threshold nature which correlated with the exciting picosecond pulse. The maximum emission was Rbser~U ved at photon energy less than E~ ( E~ is the energy gap width of the unexcited sample). As evident from Fig. 5, the emission occured at about the same W ex
625
626
Vol. 72, No. 7
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE
values at which reversible brightening oooured. In the present work reversible brightening was studied in a wider than in' range of energies of exciting photons ~ e x ; it is shown, than the results are understandable on the basis of the assumption of recombination superluminescenoe being the decisive factor. 2. The samples studied were A1 o. 5Gao. 5As - GaAs - A1 o. 5Gao. 5As heterostructures, with donor concentration in the GaAs layer of about 3.10 ~5 cm -3 and a compensation of about 60%. The substrate was etched away on a 4n~n x × 4mm area. The Alo.5Gao.5As layers, designed to stabilize the surface recombination and mechanical strength, were transparent to light with ~ < 2.2eV ~. Typical thicknesses of the heterostructure: 1.1 - 1.5 --1.1 ~m (sample No.l) 1.1 -. 2.1 0.6 ~ (sample No.2). Figs. 1-4 show the results of measurements with sample No.1, Fig.5 - with sample No.2. The results obtained with both samples were in complete agreement. Measurements were carried out on a laser differential picosecond spectrophotometer 5 at room temperature. Two light pulses, an exciting pulse and a probing pulse, were focused onto the sample at an almost right angle to its surface, with the angle between the light beams of about 8 ° and at an identical beam polarization. High-power exciting pulses of variable energy were provided by a picosecond parametric light generator. The maximal energy of a single exciting pulse (in the neral case - different for different ex) was about 100~J at a pulse duration of approximately tp~4Ops. The exciting pulse energy Wex was varied by varying the thickness of a neutral absorber with a calibrated attenuation. A light continuum pulse of about 4Ops served as t~e probing pulse; it was focused to a diameter of approximately 0.3ram and carried an energy 2 to 3 orders of magnitude lower than that of the exciting pulse. Exciting and probing pulses were generated simultaneously. The probir~ pulse propagation channel was provlded with a variable optical time delay ~d' with a zero delay corresponding to the maximum of the G(~d ) cross-correlation function of the exciting and probing pulses. The probing beam after the sample, and also the reference beam in the probi channel are focused at the input slin~ of a monochromator, whose output signals arrive at two photomultipliers and then represent the integral signals Ep and E r at a %p wavelength. Measurements alternated between the presen-
ce and absence of an exciting pulse and then the value of lg(T1/T O) = ig(E1p/E1r)/(~p/EO), where superscripts o and I denote the absence and presence of the exciting pulse, is calculated from about 60 readings. Studies of transparency variation at a wavelength kp as a function of ~d at various ~ e x disclosed the transparenoy to be approximately reversibly variable during the exciting pulse, rising during its leading edge and fallduring its trailing edge, and acquiring one and same value after the excitation is turned off, irrespective of the photon energy ~Oex (Fig. 1 ). At the same time, this resudual transparency depends on the wavelength kp of the probing beam. Subsequent variations of the transparency are according to an exponential law with a time constant of about 8OOps, this value approaching the recombination time in weakly excited samples. As evident from the measurements (Fig.2), reversible transparency variation is observed in a wide range of pulse energies and features a threshold nature in terms of W e x ° The results of transparency spectra variation measurements as a function of ~d (Pig. 3 ) indicate, that almost in the entire spectrum range,where transparency variations were observed, these variations are reversible in the ~0ex range from 1.67eV to E gO. After the excitation is removed, transparency spectrum variations acquire one and the same form,
0.4
&&A
--
A A
o
0.3z~
z~
[...
x
0.2
-
~
x x
x
x
x
0.1
~
--
x
Ax
-50
A
Xx~x
z~ ,
0
50
x
x
I 100
"rd,ps
F i g . 1 . GaAs transparency variations as a function of the delay time, at ~ p =
1.56eV: ~ e x = 1 . 6 7 e V - A, ~ e x =I.44eV-x. The solid line denotes the cross-correlation function G(~d).
V o l . 72, No. 7
627
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE @
0.3 t (a) 0.2
+~Z(SI)
0.1 ~xxx• ~ ex Xl
x
03b:
[-, [.-,
0.2
i
x
x
I
I
~ l os ~e(83) (11 P where ~ is the pz~mb~_n 6 pulse photon energy; 81 ,82,83 are the energies of
I
electrons taking part in the absorption at transitions between the bands of heavy, light and split off holes and the conduction band; 8 h, ~ are the heavy
@
and the and the
•
0.1 Ixl~ x
x I
.:) 0"ljl~X xe• xe I 0.2
x
x
x
I
I
I
g
• • x x I I 0.4 0.6 Wex, arb. units
I
x
x
I 0.8
I 1.o
F i g . 2 . Transparency variations as a function of exciting pulse energy at t~0p = 1.56eV:
a
-
NO
ex
c - ~ex=1.44eV;
=1.67eV,
b -
N~o
ex
=1o52eV
%d = 6ps - e, ~d = 80ps -
x.
~_ ~
:o
•
Io.~: '~,,° #
ioi
o
and ~h were determined from two relati-
o
, 1.5
OS
on band botton energies relative to the top of the valence band and split off band, respectively. Constants a I ,a2,a 3 were selected so as to describe the absorption spectrum of an unexcited crystal 6, taking into account the relations between masses of various holes. Energies of electrons and holes taking in absorption were calculated by the Kane fourband model, assuming J*e,fZ and fh to be Fermi functions. The curves were calculated by Eq. (I) at d = I .2~Lm, al= 3.8, ~2 = 2.1 ~3 = 2.4o104eV1/2cm -I, E g = 1.42eV, E os = 1.74eV. The botton curve corresponds to residual brightening (%d--8Ops) and was calculated assuming electrons and holes to have identical temperatures equal to that of the lattice, T = 293K. Fermi quasi-levels ~e
o
o.,1-
light hole energies; fe,fZ,fh are distributions of electrons, light heavy holes; d is the thickness of GaAs layer; E and E are conducti-
~ 1.6
1.7
, ,--~.~! 1.8 1.9
o
~,~ p, e V
Figz3. Transparency variation spectrum at ~ e x = 1.52eV: %d = 6ps - o, %d = 27 ps - X, ~d = 46pS - I, %d=8Ops - A. Solid lines denote theoretical findings.
irrespective of the energy of exciting pulses (providing it exceeds the threshold value) and, what is especially important, of the photon energy ~Oex. This latter fact is illustrated in Fig.4. 3. The measurement results shall now be discussed. Fig.3 shows the measured brightening spectra, along with the calcu1 lated under the assumption: ~ in T ~o~ -
ons: the neutrality condition (n = p) and the condition ~e- ~h = E , this latter meaning that recombination superluminescence succeeds to drop the carrier concentration to a level, corresponding to no gain, in ~d = 80ps. These two conditions set ~e = Eg+ ~h= O.052eV, n = = p = I .I °I018 om -3. The top curve was fitted to the brightening spectrum at %d=6ps and corresponds to the following parameters determining the state of electrons and holes: n= p = 3.5.1018cm-,3 ~e = 0.104eV, Eg+ ~h= O.066eV (Fermy levels are relative to the botton of the conduction band). This means that during the pulse there is a spectral band of O.038eV width where light is amplified and estimates of the maximal enhancement factor indicate k m values of about 300cm -I . The closeness of ~e- ~h and Eg values indicates that recombination superluminescence limits the carries concentration even during the excitation pulse.
628
Vol. 72, No. 7
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE
x x x
o.2l;
]~
x
,~
(a)
",,
• A 4~ °
I 1.5
Tig.4.
~
AoA ex c A &
×
~-"'-,
~ioX,.~,~, a°~ I 'A'4%~u~_ 1.6 1.7 1.8 1.9 ~,~p, eV
[-- 0.2 ---~
x
x ,
Transparency variation s ~ o t r u m at ~d = 80ps : ~ e x = l .67eV x, ex = 1.52eV - A, ~ e x = 1.44eV - e.
~
-
i
•
I
I
being
Is= A~op(~m) (kma)-2exp(kma), where p(~m ) is the number of spontaneous quanta emitted during a unit of time by a unit of volume in a frequency band unit~ A~ is the spectrum width of the gain band, k m and o~m are the maximal gain and the frequency at the gain maximum. The factor (ka) -2 takes into account the effective area of the spot, from which spontaneous emission is amplified at approximately the maximal gain. Assuming P(~m)~m/~2c2 (~m is the absorptance of the unexcited sample at the gain maximum) and using the above data we arrive at Is=(kma)-2exp(kma).1026s-1om-~ To obtain effective carrier lifetimes of about I ps, k m a has to be assumed equal to about 15, this not contradicting the above estimate of k m and an estimated number of carrier pairs generated during a time uniL in a volume unit during the action of the exciting pulse.
{
I
x
0.4 x
The region near the absorbtion edge should be excluded when comparing the theoretical and experimental findings due to experimental results here distorted by interference effects, amplified during sample brightening, while theoretical data are distorted by exiton effects, screened during excitation and unaccounted in Eq.(1). Estimates indicate superluminescence to be of importence at picosecond durations. Assuming the excited spot to be a disc of diameter "a" and thickness "d", the number of superluminescence quanta emitted during a unit time per unit of volume will be of the order of
I
x
0.2~x xjxXX {
0.1
I
{
0.2 0.3 0.4 Wex ,arb. units
I
0.5
Fig.5. Transparency variations as a function of exciting pulse energy at h£0ex= 1.49eV, hmp 1.56eV : Td = 5ps - x, • d = 60ps - e; b - Emission energy (with a photon energy of 1.406eV) as a function of exciting pulse energy at h~0ex= I. 49eV.
In conclusion it should be noted, that the observed heating of the electron/hole plasma during excitation may also be related to recombination superluminescence. Owing to this recombination mechanism, carrier extinction takes place at a zero energy, a certain part of the energy of each pair, ~ e x - E , at which it was generated, is transferred to the plasma and heats it. This heating mechanism may compete with intraband absorbtion. Thus, the present work indicates recombination superluminescence to play a decisive role in the generation of electron/hole plasma excited by picosecond light pulses in GaAs. Acknowledgements - The authors wish to express their gratitude to Yu.V.Gulyaev for his attention and support, Yu.D.Kalafatl and G.N.Shkerdin for useful discussions, and B.S.Yavich for sample preparat ion.
Vol. 72, No. 7
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE REFERENOEB
1.
2. 3.
l.L.Bronevoi, R.A.Gadonas, V.V.Krasauskas, T.M.Lifshits, A.S.Piskarskas, M.A.Sinitsin, B.S.Yavloh. Pis'ma Zh.k~k~p.Teor.Piz., 42, 322 (1985) JETP Lett.42, 395 (1985). I.L.Bronevoi, S.E.Kumekov, V.I.Perel'.Pis'ma Zh.Eksp.Teor.Fiz., 43, 368 (1986) J~'fP Left. 43, 473. N.N.Ageeva, I.L.Bronevol, E.G.Dyadyushkin, B.S.Yavioh. Pis'ma
4. 5. 6.
Zh.Eksp.Teor.Fiz. 48, 252 (1988) Lett. 48, 276 (1988). B.Monemar, K.K.Shin, G.D.Pettit. J.Appl.Phys., 47, 2604 (1976). R.Gadonas, R.Danelyus, L.Piskarskas. Kvantovaya elektronika, 8, 669 (1981 ). I.S.Blakemore. J.Appl.Phys., 53, R123 (1982).
629
Solld State Communications, Vol. 72, No. 7, pp. 625-629, Printed in Great Britain.
1989.
0038-1098/8953.00+.00 Pergamon Press plc
S U F E R ~ I N E ~ C E AND BRIGHT~ING OF GALLIUMARSENIDEUNDER I N T ~ ABSORPTIONOF PICOSECONDLIGHT 1 ~ N.N.Ageeva, I.L.Bronevoi, E.G.Dyadyushkin and V.A.Mironov Institute of Radio Engineering and Electronics, USSR Academy of Sciences, USSR, t 0 ~ 0 7 , loscow, GSP- 3, Marx Avenue, t8 S.E.Ktmekov and V.I.Perel' A.F.Ioffe Physicotechn.lcal Institute, USSR Academy of Sciences,
U~R, i94021, Lenlngraae, yoAitekhnlcheskaya St., 28 (Received iO August 1289 by A.L.Efros)
The brigh_tening of the GaAs layer caused by picosecond light ~ulses ~ s been.studied, The .brigtening spectru= just attar exitation aces n.ot depena on the energy of. the exiting pulse t i f it exceems a certain thresnoldTana on the energy l~exof the exiting photons, either. This spectrum i s completely describable under the a s s u ~ t i o n , that the photoexcited.eleosrons and holes have the e e r ~ dystriDu~ion at the Aattice temperature (295K)and with the Farmy quasilevels ~ e and ~h s a t i s i:ying the condition ~., .-~h-Eg..This ~ l o w s to conc.lude, that carrier concent~ration is limitem Dy the recombination superluminescence. •~ne oDser~.ation.of the edge emission that correlated with the exciting puAse of' picosecund duration confirms this conoAuslon.
I. Approximately reversible brightening of a gallium arsenide layer under excitation by high-power picosecond light pulses with a photon energy ~ e x slightly exceeding the energy gap E width has been observed by I.Bronevoi et al I . During the pulse, the brightening is the higher, the greater is the exciting energy. Inluediately after the excitation pulse a residual brightening in a wide spectrum band is observed, this including transitions between the split off valence and conduction bands. The complete spectrum was independent of the exciting pulse energy, if this energy was above a certain tresh-_ old value. These results are explained ~ under the assumption that during almost the entire high-power pulse saturation was present, this meaning that Fermi quasi-levels of electrons and holes meet the condition ~e- ~ h = ~ e x ' which correspond to complete brightening of the layer for the exciting light. Another possible cause of revereible brightening (also mentioned in2) is related to recombination induced by superluminesoenoe. Even before saturation is established, at We- ~ > E , in the spectral band
E < ~ < Pe- ~ population inversion occurs which can result in superluminesoenoe. Under such conditions each spontaneous emission photon induces recombination of a large number (of the order of exp(ka), where "k" is the enhancement factor and "a" is the diameter of the light spot) of electron-hole pairs. The effective recombination time may be rather short. Experimental results I did not allow to distinguish between condition ~e- ~ = ~ e x (saturati°n) and ~e- ~ = E (complete control by superluminesoenoe), since in these experiments I the difference ~ e x - E g was less than the thermal energy of carriers kT. The significant role of recombination superluminescence is strongly confirmed by anomalous emission of excited GaAs layers 3 of a threshold nature which correlated with the exciting picosecond pulse. The maximum emission was Rbser~U ved at photon energy less than E~ ( E~ is the energy gap width of the unexcited sample). As evident from Fig. 5, the emission occured at about the same W ex
625
626
Vol. 72, No. 7
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE
values at which reversible brightening oooured. In the present work reversible brightening was studied in a wider than in' range of energies of exciting photons ~ e x ; it is shown, than the results are understandable on the basis of the assumption of recombination superluminescenoe being the decisive factor. 2. The samples studied were A1 o. 5Gao. 5As - GaAs - A1 o. 5Gao. 5As heterostructures, with donor concentration in the GaAs layer of about 3.10 ~5 cm -3 and a compensation of about 60%. The substrate was etched away on a 4n~n x × 4mm area. The Alo.5Gao.5As layers, designed to stabilize the surface recombination and mechanical strength, were transparent to light with ~ < 2.2eV ~. Typical thicknesses of the heterostructure: 1.1 - 1.5 --1.1 ~m (sample No.l) 1.1 -. 2.1 0.6 ~ (sample No.2). Figs. 1-4 show the results of measurements with sample No.1, Fig.5 - with sample No.2. The results obtained with both samples were in complete agreement. Measurements were carried out on a laser differential picosecond spectrophotometer 5 at room temperature. Two light pulses, an exciting pulse and a probing pulse, were focused onto the sample at an almost right angle to its surface, with the angle between the light beams of about 8 ° and at an identical beam polarization. High-power exciting pulses of variable energy were provided by a picosecond parametric light generator. The maximal energy of a single exciting pulse (in the neral case - different for different ex) was about 100~J at a pulse duration of approximately tp~4Ops. The exciting pulse energy Wex was varied by varying the thickness of a neutral absorber with a calibrated attenuation. A light continuum pulse of about 4Ops served as t~e probing pulse; it was focused to a diameter of approximately 0.3ram and carried an energy 2 to 3 orders of magnitude lower than that of the exciting pulse. Exciting and probing pulses were generated simultaneously. The probir~ pulse propagation channel was provlded with a variable optical time delay ~d' with a zero delay corresponding to the maximum of the G(~d ) cross-correlation function of the exciting and probing pulses. The probing beam after the sample, and also the reference beam in the probi channel are focused at the input slin~ of a monochromator, whose output signals arrive at two photomultipliers and then represent the integral signals Ep and E r at a %p wavelength. Measurements alternated between the presen-
ce and absence of an exciting pulse and then the value of lg(T1/T O) = ig(E1p/E1r)/(~p/EO), where superscripts o and I denote the absence and presence of the exciting pulse, is calculated from about 60 readings. Studies of transparency variation at a wavelength kp as a function of ~d at various ~ e x disclosed the transparenoy to be approximately reversibly variable during the exciting pulse, rising during its leading edge and fallduring its trailing edge, and acquiring one and same value after the excitation is turned off, irrespective of the photon energy ~Oex (Fig. 1 ). At the same time, this resudual transparency depends on the wavelength kp of the probing beam. Subsequent variations of the transparency are according to an exponential law with a time constant of about 8OOps, this value approaching the recombination time in weakly excited samples. As evident from the measurements (Fig.2), reversible transparency variation is observed in a wide range of pulse energies and features a threshold nature in terms of W e x ° The results of transparency spectra variation measurements as a function of ~d (Pig. 3 ) indicate, that almost in the entire spectrum range,where transparency variations were observed, these variations are reversible in the ~0ex range from 1.67eV to E gO. After the excitation is removed, transparency spectrum variations acquire one and the same form,
0.4
&&A
--
A A
o
0.3z~
z~
[...
x
0.2
-
~
x x
x
x
x
0.1
~
--
x
Ax
-50
A
Xx~x
z~ ,
0
50
x
x
I 100
"rd,ps
F i g . 1 . GaAs transparency variations as a function of the delay time, at ~ p =
1.56eV: ~ e x = 1 . 6 7 e V - A, ~ e x =I.44eV-x. The solid line denotes the cross-correlation function G(~d).
V o l . 72, No. 7
627
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE @
0.3 t (a) 0.2
+~Z(SI)
0.1 ~xxx• ~ ex Xl
x
03b:
[-, [.-,
0.2
i
x
x
I
I
~ l os ~e(83) (11 P where ~ is the pz~mb~_n 6 pulse photon energy; 81 ,82,83 are the energies of
I
electrons taking part in the absorption at transitions between the bands of heavy, light and split off holes and the conduction band; 8 h, ~ are the heavy
@
and the and the
•
0.1 Ixl~ x
x I
.:) 0"ljl~X xe• xe I 0.2
x
x
x
I
I
I
g
• • x x I I 0.4 0.6 Wex, arb. units
I
x
x
I 0.8
I 1.o
F i g . 2 . Transparency variations as a function of exciting pulse energy at t~0p = 1.56eV:
a
-
NO
ex
c - ~ex=1.44eV;
=1.67eV,
b -
N~o
ex
=1o52eV
%d = 6ps - e, ~d = 80ps -
x.
~_ ~
:o
•
Io.~: '~,,° #
ioi
o
and ~h were determined from two relati-
o
, 1.5
OS
on band botton energies relative to the top of the valence band and split off band, respectively. Constants a I ,a2,a 3 were selected so as to describe the absorption spectrum of an unexcited crystal 6, taking into account the relations between masses of various holes. Energies of electrons and holes taking in absorption were calculated by the Kane fourband model, assuming J*e,fZ and fh to be Fermi functions. The curves were calculated by Eq. (I) at d = I .2~Lm, al= 3.8, ~2 = 2.1 ~3 = 2.4o104eV1/2cm -I, E g = 1.42eV, E os = 1.74eV. The botton curve corresponds to residual brightening (%d--8Ops) and was calculated assuming electrons and holes to have identical temperatures equal to that of the lattice, T = 293K. Fermi quasi-levels ~e
o
o.,1-
light hole energies; fe,fZ,fh are distributions of electrons, light heavy holes; d is the thickness of GaAs layer; E and E are conducti-
~ 1.6
1.7
, ,--~.~! 1.8 1.9
o
~,~ p, e V
Figz3. Transparency variation spectrum at ~ e x = 1.52eV: %d = 6ps - o, %d = 27 ps - X, ~d = 46pS - I, %d=8Ops - A. Solid lines denote theoretical findings.
irrespective of the energy of exciting pulses (providing it exceeds the threshold value) and, what is especially important, of the photon energy ~Oex. This latter fact is illustrated in Fig.4. 3. The measurement results shall now be discussed. Fig.3 shows the measured brightening spectra, along with the calcu1 lated under the assumption: ~ in T ~o~ -
ons: the neutrality condition (n = p) and the condition ~e- ~h = E , this latter meaning that recombination superluminescence succeeds to drop the carrier concentration to a level, corresponding to no gain, in ~d = 80ps. These two conditions set ~e = Eg+ ~h= O.052eV, n = = p = I .I °I018 om -3. The top curve was fitted to the brightening spectrum at %d=6ps and corresponds to the following parameters determining the state of electrons and holes: n= p = 3.5.1018cm-,3 ~e = 0.104eV, Eg+ ~h= O.066eV (Fermy levels are relative to the botton of the conduction band). This means that during the pulse there is a spectral band of O.038eV width where light is amplified and estimates of the maximal enhancement factor indicate k m values of about 300cm -I . The closeness of ~e- ~h and Eg values indicates that recombination superluminescence limits the carries concentration even during the excitation pulse.
628
Vol. 72, No. 7
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE
x x x
o.2l;
]~
x
,~
(a)
",,
• A 4~ °
I 1.5
Tig.4.
~
AoA ex c A &
×
~-"'-,
~ioX,.~,~, a°~ I 'A'4%~u~_ 1.6 1.7 1.8 1.9 ~,~p, eV
[-- 0.2 ---~
x
x ,
Transparency variation s ~ o t r u m at ~d = 80ps : ~ e x = l .67eV x, ex = 1.52eV - A, ~ e x = 1.44eV - e.
~
-
i
•
I
I
being
Is= A~op(~m) (kma)-2exp(kma), where p(~m ) is the number of spontaneous quanta emitted during a unit of time by a unit of volume in a frequency band unit~ A~ is the spectrum width of the gain band, k m and o~m are the maximal gain and the frequency at the gain maximum. The factor (ka) -2 takes into account the effective area of the spot, from which spontaneous emission is amplified at approximately the maximal gain. Assuming P(~m)~m/~2c2 (~m is the absorptance of the unexcited sample at the gain maximum) and using the above data we arrive at Is=(kma)-2exp(kma).1026s-1om-~ To obtain effective carrier lifetimes of about I ps, k m a has to be assumed equal to about 15, this not contradicting the above estimate of k m and an estimated number of carrier pairs generated during a time uniL in a volume unit during the action of the exciting pulse.
{
I
x
0.4 x
The region near the absorbtion edge should be excluded when comparing the theoretical and experimental findings due to experimental results here distorted by interference effects, amplified during sample brightening, while theoretical data are distorted by exiton effects, screened during excitation and unaccounted in Eq.(1). Estimates indicate superluminescence to be of importence at picosecond durations. Assuming the excited spot to be a disc of diameter "a" and thickness "d", the number of superluminescence quanta emitted during a unit time per unit of volume will be of the order of
I
x
0.2~x xjxXX {
0.1
I
{
0.2 0.3 0.4 Wex ,arb. units
I
0.5
Fig.5. Transparency variations as a function of exciting pulse energy at h£0ex= 1.49eV, hmp 1.56eV : Td = 5ps - x, • d = 60ps - e; b - Emission energy (with a photon energy of 1.406eV) as a function of exciting pulse energy at h~0ex= I. 49eV.
In conclusion it should be noted, that the observed heating of the electron/hole plasma during excitation may also be related to recombination superluminescence. Owing to this recombination mechanism, carrier extinction takes place at a zero energy, a certain part of the energy of each pair, ~ e x - E , at which it was generated, is transferred to the plasma and heats it. This heating mechanism may compete with intraband absorbtion. Thus, the present work indicates recombination superluminescence to play a decisive role in the generation of electron/hole plasma excited by picosecond light pulses in GaAs. Acknowledgements - The authors wish to express their gratitude to Yu.V.Gulyaev for his attention and support, Yu.D.Kalafatl and G.N.Shkerdin for useful discussions, and B.S.Yavich for sample preparat ion.
Vol. 72, No. 7
SUPERLUMINESCENCE AND BRIGHTENING OF GALLIUM ARSENIDE REFERENOEB
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