- Email: [email protected]
Wavelength dependence of picosecond absorption saturation in gallium arsenide
Solid State Communications, Vol. 49, No. 2, pp. 141-143, 1984. Printed in Great Britain.
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
WAVELENGTH DEPENDENCE OF PICOSECOND ABSORPTION SATURATION IN GALLIUM ARSENIDE C. Minot, J. Chavignon, H. le Person and J.L. Oudar Centre National d'Etudes des T616communications, Laboratoire de Bagneux, 196 rue de Paris, 92220 Bagneux, France (Received 8 September 1983 by M. Balkanski) Absorption saturation in the picosecond regime has been observed in GaAs MBE-grown epitaxial layers at low temperature, and its wavelength dependence in the range 700-820 nm has been observed using 7 psec pulses from a tunable infrared LilO3 parametric generator. For peak intensities up to 1 GW cm -2 almost complete saturation of band-to-band absorption could be achieved without damaging the sample. Although the direct saturation of optically coupled states is expected to become the dominant contribution in the ultrashort limit, our experimental results are quantitatively described with the band-filling model, which includes the dynamic Burstein shift and bandgap renormalization. OPTICAL ABSORPTION SATURATION has been studied in various semi-conductors and with various pulse durations: in InSb with a CW laser [1]; in GaAs [2], GaP [3], InSb [4] with nanosecond or subnanosecond pulses; in InAsxPl_ x [5], Gal_xln~As [5], HgxCdl_~Te [6], Ge [7] with picosecond pulses. Such a saturation of optical absorption can occur as a result of two possible mechanisms, depending on the pulsewidth At: (1) Self-induced transparency for At shorter than the decay-time T2 of the induced polarization. (2) Occupation of states by photoexcited carriers for longer At. Only part of the electronic states are directly involved in the optical transition, and the absorption saturation depends on the population of these states only. If At is long enough, an electron-hole plasma is formed, which fills the band states up to the energy level of the optically-coupled states (dynamic Burstein effect). If not, the photoexcited carriers remain in the opticallycoupled states during a significant part of the pulse duration; this effect has been termed state-filling, as opposed to the band-filling associated with thermalized distributions [8]. At present, little is known about the relative magnitude of these last two contributions, which in fact should depend on many parameters such as excitation wavelength and intensity, crystal quality, temperature, etc. In this letter, we report observation of absorption saturation in GaAs in the picosecond regime, as a function of photon excess energy above the gap. The bandfilling model gives a fair account of our data. We emphasize that under short pulse excitation, the carrier density can be connected to the incident light intensity neglecting any recombination or diffusion process, in contrast to the nanosecond or CW regimes.
The optical source used for these experiments is a picosecond parametric generator. It consists of two LilO3 crystals pumped at 0.53/am by a single 22 psec pulse, obtained after extraction, amplication and frequency doubling from a passively mode-locked Nd : YAG laser. The parametric generator provides pulses tunable between 0.7-2/am, with ~ 10/aJ energy, 7 psec pulsewidth, 15 A bandwidth and 3 Hz repetition rate in the vicinity of 0.8/am. The output beam is focused on the sample with a spotsize ~ 10 -3 cm 2. The sample is a 1.5/am thick GaAs layer sandwiched between two AlxGal_xAs layers (x = 0.35), grown by molecular beam epitaxy on a GaAs substrate. These layers are unintentionally doped, with p-type residual doping of ~ 10 Is cm -3. A 1 mm 2 area of the substrate is selectively etched away so that the epitaxial thin layers can be studied in transmission. Further, for photon energies hv below the AlxGal_xAs bandgap but above the GaAs bandgap, optical absorption is sensitive to band-to-band transitions in the GaAs layer only, and we have restricted our measurements to that spectral range. Both the incident and transmitted pulse energies E i and E t were measured with Si photodiodes. The time integrated signals for each shot were digitized and transferred to a computer which could also control a stepping motor for wavelength tuning. Neutral density filters as well as the laser output fluctuations were used to vary the incident power. The sample was maintained at liquid helium temperature. The experimental method consisted in recording the incident and transmitted pulse energies at a fixed wavelength. In Fig. 1, the ratio Et/E i is plotted as a function of Ei for different photon excess energies above the gap A E = (hu --Eg); each point is an average of 20 laser
141
142
DEPENDENCE OF ABSORPTION SATURATION IN GALLIUM ARSENIDE 0
fiaAs
l,.2K
respectively. Limiting the expansion in the r.h.s, of equation (2a) to the first term, which does exhibit a saturation behavior, enables us to solve the propagation equation exactly:
o o DO o o ~ o
0
o t/3
f
0 .¢'/
z
o
r.~
0
[]
~OO 0
" v
0
~-
v
N ot(N)
F[z(N)] -
._=.8
(3. 0
mOrlElrlD
DDtn
oO
000000--
O
v *
1.2
i
i
i
i
9
i
.01
i
i
.1
INCIDENT ENERSY
i
~'
z(N) =
i
i
Vol. 49, No. 2
i
1
i
L
10
{ p J/pro z )
Fig. 1. Absorption saturation data for GaAs at 4.2 K, at different wavelengths: (o) AE = 1 meV; (zx) AE = 10meV; (o) AE = 40 meV; (o) AE = 100meV; (v) ,SE = 270meV. The curve at AE = 10meV is a fit using the model described in the text, with a plasma temperature T = 90K. shots. One observes an increase of transmission with increasing pump power above a rather well-defined threshold, until complete bleaching occurs; the onset of saturation moves to higher powers for larger AE. No optical damaging of the sample occurred at fluences up to 15 mJ cm -2. The time evolution and spatial variation of the carrier density N and of the radiation intensity I can be described by rate equations: aN I(z, t) "~- (z, t) = ot(z, t) h--~
(1 a)
dl ~z (z, t) = -- ot(z, t) I(z, t),
(1 b)
where ot(z, t) is the absorption coefficient at photon energy hv, depth z and time t. In equation (lh), we have neglected any kind of carrier loss e.g. recombination or diffusion; this is legitimate during the optical pulse and for not too high carrier concentrations or carried concentration gradients (for example the lifetime associated with bimolecular recombination is "" 120 psec at 5 x 1017cm -3 [2]). Now if the absorption coefficient depends on the carrier density only, i.e. ot(z, t) = a[N(z, t)], then equations (la) and (lb) can be integrated over time and transformed into: dot N(z) = ot[N(z)] F(z) -- ½ot[N(z)] ~ [N(z)]Y2(z) + . . .
(3a)
1
1
a(No)
ot(N)
N f 1%
dn (3b)
not(n)
with No = ot(N0)F(0). Then equations (3a) and (3b) describe optical saturation, provided we know the Ndependence of ot; this is just what is given by the bandfilling model. In this case equations (3a) and (3b) yield a rather good approximation to the exact solution of equations (2a) and (2b). This point has been checked for a few typical cases. In the band-filling model [9], electrons and holes are in thermal equilibrium among themselves due to e - e , h - h and e - h collisions, at a temperature Thigher than the lattice temperature TL. They have a Fermi-Dirac distribution function: f/(E) =
1 + e x p ~ k r ]J
i=e,h
(4)
where E i is the chemical potential of particle i. The wellknown formula: N = ~-~2~'-~-]
f/(E),v/-ff dE
i = e, h
(5)
expresses the carrier density in a parabolic band, with effective mass mi, as a function of chemical potential and temperature. Using a two band approximation, the absorption spectrum is given by: ot(hv) = oto(hv)
--re - -
1+me
\
mh/
--fh
-+ mh
\
(6) '
me/J
where E~ is the renormalized bandgap [2] and oto the low-level absorption coefficient. Two-particle interactions, which definitely modify the band picture, are included here in the value of oto and in the bandgap renormalization; however the carried density is fixed by the band density of states. Saturation takes place when E t ~ (hv --E~)/(1 + rni/mj), i.e. when the optically coupled states become appreciably populated. We calculate the plasma chemical potential tt(N) at temperature T [10]:
(2a). IJ(N)T = E~(N) + Ee(N)T + Eh(N)T (7) (2b) This quantity is related to our experimental results, for at the onset of saturation we can determine the average where N(z) = N(z, co) and F(z) = f+_=I(z, t)[hv dt are the carrier density in the sample: carrier density (after the pulse) and the photon fluence
dF --~z (Z) = - - N ( z )
Vol. 49, No, 2
DEPENDENCE OF ABSORPTION SATURATION IN GALLIUM ARSENIDE
CHEMIEALPOTENTIAL p -Egap (meV) 1
i
~o
i
~oo 1
i
100 -
'?,
..
-
6%
J
"- 10 ,,nQ "
t-t
"-
1
u_°
.%~"
"=' (Z
'
1
Mz I
1
10 h v - E gap
I
I
100 (meV)
Fig. 2. Experimental points are fluences at the onset of saturation at different wavelengths and refer to the left vertical and lower horizontal logarithmic scales. The curves are obtained using equation (7) and refer to the right vertical and upper horizontal scales. The average carrier density is related to the photon fluence via equation (8). l
--
/V = a o ( 1 - - R ) F o n s e t -
e-a°d
saturation, in agreement with the model proposed by Shah et al. [12]. Under so strong excitations other mechanisms, such as state-filling, might competitively contribute to saturation; however only shorter pulse durations, resulting in lower carrier densities under similar excitation intensities, could clearly demonstrate these contributions. In conclusion, the band-filling model, including bandgap renormalization and dynamic Burstein shift, adequately describes absorption saturation in GaAs for pulse durations down to 7 psec. In this regime the carrier density is easily inferred from the photon fluence. The results give clear evidence of carrier heating. It should be noted that these single beam experiments are not sensitive enough to precisely evaluate the state-filling contributions. Other experimental configurations such as fourwave mixing are more appropriate to this purpose [13]. Preliminary results in our laboratory confirm that very fast contributions can be isolated in this way [14].
Acknowledgement - We are very grateful to Dr F. Alexandre who prepared the MBE sample investigated in this work. REFERENCES
(8)
1.
(R is the reflection coefficient, d the sample thickness), as well as the chemical potential:/a "" hu. In Fig. 2 experimental points and calculated curve for T = 45 K are superimposed. Further the complete model enables us to fit the saturation curves as shown in Fig. 1. A surprisingly good agreement is obtained especially in Fig. 2: we conclude that absorption saturation under 7 psec excitation occurs at carrier densities consistent with valence and conduction band filling. The fit is not very sensitive to the value of temperature for large AE, whereas at small AE (AE ~ kT) the condition/a "~ hu is not precisely fullfilled; however for AE < 20 meV we can estimate the electron-hole plasma temperature to be 45 K at the onset of saturation, a value for which the plasma cooling rate is strongly reduced [11 ]. We have fitted the entire saturation curve AE = 10 meV (Fig. 1) with a unique temperature T = 90 K. For AE = 40 meV we find T = 120 K. This discrepancy with the previous result indicates that a higher temperature is achieved at photon fluences above the onset of
2.
aod
143
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
P. Lavallard, R. Bichard & C. Benoit h la Guillaume, Phys. Rev. B16, 2804 (1977). J. Shah, R.F. Leheny & C. Lin, Solid State Commun. 18, 1035 (1976). A.K. Kar, M.F. Kimmit & A.A. Serafetinides, Opt. Commun. 37,277(1981). A.V. Nurmikko, Opt. Commun. 16,365 (1976). J.F. Reintjes, J.C. Mc Groddy & A.E. Blakeslee, J. Appl. Phys. 46,879 (1975). J.C. Matter, A.L. Smirl & M.O. Scully, Appl. Phys. Lett. 28,507 (1976). A. Elci, M.O. Scully, A.L. Smirl & J.C. Matter, Phys. Rev. BI6, 191 (1977). D.K. Ferry, Phys. Rev. BI8, 7033 (1978). R.N. Zitter, Appl. Phys. Lett. 14, 73 (1969). J. Shah, R.F. Leheny & W. Wiegmann, Phys. Rev. B16, 1577 (1977). E.O. Goebel & O. Hildebrand, Phys. Status Solidi (b) 88, 645 (1978). J. Shah, C. Lin, R.F. Leheny & A.E. Di Giovanni, Solid State Commun. 18,487 (1976). A.L. Smirl, T.F. Boggess, B.S. Wherrett, G.P. Perryman & A. Miller, Phys. Rev. Lett. 49,933 (1982). J.L. Oudar, I. Abram & C. Minot (to be published) published).
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
WAVELENGTH DEPENDENCE OF PICOSECOND ABSORPTION SATURATION IN GALLIUM ARSENIDE C. Minot, J. Chavignon, H. le Person and J.L. Oudar Centre National d'Etudes des T616communications, Laboratoire de Bagneux, 196 rue de Paris, 92220 Bagneux, France (Received 8 September 1983 by M. Balkanski) Absorption saturation in the picosecond regime has been observed in GaAs MBE-grown epitaxial layers at low temperature, and its wavelength dependence in the range 700-820 nm has been observed using 7 psec pulses from a tunable infrared LilO3 parametric generator. For peak intensities up to 1 GW cm -2 almost complete saturation of band-to-band absorption could be achieved without damaging the sample. Although the direct saturation of optically coupled states is expected to become the dominant contribution in the ultrashort limit, our experimental results are quantitatively described with the band-filling model, which includes the dynamic Burstein shift and bandgap renormalization. OPTICAL ABSORPTION SATURATION has been studied in various semi-conductors and with various pulse durations: in InSb with a CW laser [1]; in GaAs [2], GaP [3], InSb [4] with nanosecond or subnanosecond pulses; in InAsxPl_ x [5], Gal_xln~As [5], HgxCdl_~Te [6], Ge [7] with picosecond pulses. Such a saturation of optical absorption can occur as a result of two possible mechanisms, depending on the pulsewidth At: (1) Self-induced transparency for At shorter than the decay-time T2 of the induced polarization. (2) Occupation of states by photoexcited carriers for longer At. Only part of the electronic states are directly involved in the optical transition, and the absorption saturation depends on the population of these states only. If At is long enough, an electron-hole plasma is formed, which fills the band states up to the energy level of the optically-coupled states (dynamic Burstein effect). If not, the photoexcited carriers remain in the opticallycoupled states during a significant part of the pulse duration; this effect has been termed state-filling, as opposed to the band-filling associated with thermalized distributions [8]. At present, little is known about the relative magnitude of these last two contributions, which in fact should depend on many parameters such as excitation wavelength and intensity, crystal quality, temperature, etc. In this letter, we report observation of absorption saturation in GaAs in the picosecond regime, as a function of photon excess energy above the gap. The bandfilling model gives a fair account of our data. We emphasize that under short pulse excitation, the carrier density can be connected to the incident light intensity neglecting any recombination or diffusion process, in contrast to the nanosecond or CW regimes.
The optical source used for these experiments is a picosecond parametric generator. It consists of two LilO3 crystals pumped at 0.53/am by a single 22 psec pulse, obtained after extraction, amplication and frequency doubling from a passively mode-locked Nd : YAG laser. The parametric generator provides pulses tunable between 0.7-2/am, with ~ 10/aJ energy, 7 psec pulsewidth, 15 A bandwidth and 3 Hz repetition rate in the vicinity of 0.8/am. The output beam is focused on the sample with a spotsize ~ 10 -3 cm 2. The sample is a 1.5/am thick GaAs layer sandwiched between two AlxGal_xAs layers (x = 0.35), grown by molecular beam epitaxy on a GaAs substrate. These layers are unintentionally doped, with p-type residual doping of ~ 10 Is cm -3. A 1 mm 2 area of the substrate is selectively etched away so that the epitaxial thin layers can be studied in transmission. Further, for photon energies hv below the AlxGal_xAs bandgap but above the GaAs bandgap, optical absorption is sensitive to band-to-band transitions in the GaAs layer only, and we have restricted our measurements to that spectral range. Both the incident and transmitted pulse energies E i and E t were measured with Si photodiodes. The time integrated signals for each shot were digitized and transferred to a computer which could also control a stepping motor for wavelength tuning. Neutral density filters as well as the laser output fluctuations were used to vary the incident power. The sample was maintained at liquid helium temperature. The experimental method consisted in recording the incident and transmitted pulse energies at a fixed wavelength. In Fig. 1, the ratio Et/E i is plotted as a function of Ei for different photon excess energies above the gap A E = (hu --Eg); each point is an average of 20 laser
141
142
DEPENDENCE OF ABSORPTION SATURATION IN GALLIUM ARSENIDE 0
fiaAs
l,.2K
respectively. Limiting the expansion in the r.h.s, of equation (2a) to the first term, which does exhibit a saturation behavior, enables us to solve the propagation equation exactly:
o o DO o o ~ o
0
o t/3
f
0 .¢'/
z
o
r.~
0
[]
~OO 0
" v
0
~-
v
N ot(N)
F[z(N)] -
._=.8
(3. 0
mOrlElrlD
DDtn
oO
000000--
O
v *
1.2
i
i
i
i
9
i
.01
i
i
.1
INCIDENT ENERSY
i
~'
z(N) =
i
i
Vol. 49, No. 2
i
1
i
L
10
{ p J/pro z )
Fig. 1. Absorption saturation data for GaAs at 4.2 K, at different wavelengths: (o) AE = 1 meV; (zx) AE = 10meV; (o) AE = 40 meV; (o) AE = 100meV; (v) ,SE = 270meV. The curve at AE = 10meV is a fit using the model described in the text, with a plasma temperature T = 90K. shots. One observes an increase of transmission with increasing pump power above a rather well-defined threshold, until complete bleaching occurs; the onset of saturation moves to higher powers for larger AE. No optical damaging of the sample occurred at fluences up to 15 mJ cm -2. The time evolution and spatial variation of the carrier density N and of the radiation intensity I can be described by rate equations: aN I(z, t) "~- (z, t) = ot(z, t) h--~
(1 a)
dl ~z (z, t) = -- ot(z, t) I(z, t),
(1 b)
where ot(z, t) is the absorption coefficient at photon energy hv, depth z and time t. In equation (lh), we have neglected any kind of carrier loss e.g. recombination or diffusion; this is legitimate during the optical pulse and for not too high carrier concentrations or carried concentration gradients (for example the lifetime associated with bimolecular recombination is "" 120 psec at 5 x 1017cm -3 [2]). Now if the absorption coefficient depends on the carrier density only, i.e. ot(z, t) = a[N(z, t)], then equations (la) and (lb) can be integrated over time and transformed into: dot N(z) = ot[N(z)] F(z) -- ½ot[N(z)] ~ [N(z)]Y2(z) + . . .
(3a)
1
1
a(No)
ot(N)
N f 1%
dn (3b)
not(n)
with No = ot(N0)F(0). Then equations (3a) and (3b) describe optical saturation, provided we know the Ndependence of ot; this is just what is given by the bandfilling model. In this case equations (3a) and (3b) yield a rather good approximation to the exact solution of equations (2a) and (2b). This point has been checked for a few typical cases. In the band-filling model [9], electrons and holes are in thermal equilibrium among themselves due to e - e , h - h and e - h collisions, at a temperature Thigher than the lattice temperature TL. They have a Fermi-Dirac distribution function: f/(E) =
1 + e x p ~ k r ]J
i=e,h
(4)
where E i is the chemical potential of particle i. The wellknown formula: N = ~-~2~'-~-]
f/(E),v/-ff dE
i = e, h
(5)
expresses the carrier density in a parabolic band, with effective mass mi, as a function of chemical potential and temperature. Using a two band approximation, the absorption spectrum is given by: ot(hv) = oto(hv)
--re - -
1+me
\
mh/
--fh
-+ mh
\
(6) '
me/J
where E~ is the renormalized bandgap [2] and oto the low-level absorption coefficient. Two-particle interactions, which definitely modify the band picture, are included here in the value of oto and in the bandgap renormalization; however the carried density is fixed by the band density of states. Saturation takes place when E t ~ (hv --E~)/(1 + rni/mj), i.e. when the optically coupled states become appreciably populated. We calculate the plasma chemical potential tt(N) at temperature T [10]:
(2a). IJ(N)T = E~(N) + Ee(N)T + Eh(N)T (7) (2b) This quantity is related to our experimental results, for at the onset of saturation we can determine the average where N(z) = N(z, co) and F(z) = f+_=I(z, t)[hv dt are the carrier density in the sample: carrier density (after the pulse) and the photon fluence
dF --~z (Z) = - - N ( z )
Vol. 49, No, 2
DEPENDENCE OF ABSORPTION SATURATION IN GALLIUM ARSENIDE
CHEMIEALPOTENTIAL p -Egap (meV) 1
i
~o
i
~oo 1
i
100 -
'?,
..
-
6%
J
"- 10 ,,nQ "
t-t
"-
1
u_°
.%~"
"=' (Z
'
1
Mz I
1
10 h v - E gap
I
I
100 (meV)
Fig. 2. Experimental points are fluences at the onset of saturation at different wavelengths and refer to the left vertical and lower horizontal logarithmic scales. The curves are obtained using equation (7) and refer to the right vertical and upper horizontal scales. The average carrier density is related to the photon fluence via equation (8). l
--
/V = a o ( 1 - - R ) F o n s e t -
e-a°d
saturation, in agreement with the model proposed by Shah et al. [12]. Under so strong excitations other mechanisms, such as state-filling, might competitively contribute to saturation; however only shorter pulse durations, resulting in lower carrier densities under similar excitation intensities, could clearly demonstrate these contributions. In conclusion, the band-filling model, including bandgap renormalization and dynamic Burstein shift, adequately describes absorption saturation in GaAs for pulse durations down to 7 psec. In this regime the carrier density is easily inferred from the photon fluence. The results give clear evidence of carrier heating. It should be noted that these single beam experiments are not sensitive enough to precisely evaluate the state-filling contributions. Other experimental configurations such as fourwave mixing are more appropriate to this purpose [13]. Preliminary results in our laboratory confirm that very fast contributions can be isolated in this way [14].
Acknowledgement - We are very grateful to Dr F. Alexandre who prepared the MBE sample investigated in this work. REFERENCES
(8)
1.
(R is the reflection coefficient, d the sample thickness), as well as the chemical potential:/a "" hu. In Fig. 2 experimental points and calculated curve for T = 45 K are superimposed. Further the complete model enables us to fit the saturation curves as shown in Fig. 1. A surprisingly good agreement is obtained especially in Fig. 2: we conclude that absorption saturation under 7 psec excitation occurs at carrier densities consistent with valence and conduction band filling. The fit is not very sensitive to the value of temperature for large AE, whereas at small AE (AE ~ kT) the condition/a "~ hu is not precisely fullfilled; however for AE < 20 meV we can estimate the electron-hole plasma temperature to be 45 K at the onset of saturation, a value for which the plasma cooling rate is strongly reduced [11 ]. We have fitted the entire saturation curve AE = 10 meV (Fig. 1) with a unique temperature T = 90 K. For AE = 40 meV we find T = 120 K. This discrepancy with the previous result indicates that a higher temperature is achieved at photon fluences above the onset of
2.
aod
143
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
P. Lavallard, R. Bichard & C. Benoit h la Guillaume, Phys. Rev. B16, 2804 (1977). J. Shah, R.F. Leheny & C. Lin, Solid State Commun. 18, 1035 (1976). A.K. Kar, M.F. Kimmit & A.A. Serafetinides, Opt. Commun. 37,277(1981). A.V. Nurmikko, Opt. Commun. 16,365 (1976). J.F. Reintjes, J.C. Mc Groddy & A.E. Blakeslee, J. Appl. Phys. 46,879 (1975). J.C. Matter, A.L. Smirl & M.O. Scully, Appl. Phys. Lett. 28,507 (1976). A. Elci, M.O. Scully, A.L. Smirl & J.C. Matter, Phys. Rev. BI6, 191 (1977). D.K. Ferry, Phys. Rev. BI8, 7033 (1978). R.N. Zitter, Appl. Phys. Lett. 14, 73 (1969). J. Shah, R.F. Leheny & W. Wiegmann, Phys. Rev. B16, 1577 (1977). E.O. Goebel & O. Hildebrand, Phys. Status Solidi (b) 88, 645 (1978). J. Shah, C. Lin, R.F. Leheny & A.E. Di Giovanni, Solid State Commun. 18,487 (1976). A.L. Smirl, T.F. Boggess, B.S. Wherrett, G.P. Perryman & A. Miller, Phys. Rev. Lett. 49,933 (1982). J.L. Oudar, I. Abram & C. Minot (to be published) published).