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Picosecond luminescence studies of vertical transport in short-period superlattices
Superlattices and Microstructures, Vol. 9, No. 4, 1991
503
PICOSECOND LUMINESCENCE STUDIES OF VERTICAL TRANSPORT IN SHORT-PERIOD SUPERLATTICES J. Puls (a), F. Henneber9er [a), I. N. Uraltsev (b), and A. M. Vaslllev (b] (a) H u m b o l d t - U n i v e r s i t y , D e p a r t m e n t of Physics, I n v a l i d e n s t r . 110, 1040 Berlin, GDR, and (b) A. F. I of f e P h y s i c o - T e c h n i c a l I n s t i t u t e , Academy of Sciences, 194021 L e n i n 9 r a d , USSR (Received 13 August 1990)
Photoluminescence studies with ps-time resolution are reported for three different types of GaAs-AIGaAs microstructures: (i) a short-period superlattice, (ii) a superlattice, where an enlarged well is introduced into the center, and, (iii) a superlattice, where this well is separated from the superlattice by enlar9ed barriers. Ex~:itin9 the samples by a mode-locked Ar + laser very high sensitivity is achieved by an electrooptical cross-correlation technique usin 9 a 9ain modulated Si avalanche photodiode as a detector. From the data obtained we are able to determine the relevant parameters of vertical transport and nonradiative recombination in the respective structures.
1. Introduction Time-resolved photoluminescence experiments are a powerful tool to study different aspects of carrier kinetics in semiconductor microstructures like e. 9, carrier relaxation [1,23, tunnelin 9 between coupled quantum wells [3,4], capture of carriers into the quantum well E53, and their transport perpendicular to the layers of a superlattice (SL) [6]. In the latter case, usually, an enlarged well (EW) is incorporated into the SL [7] to detect the arrival of the photo-excited carriers at the position of the EW. Here, we report on comparative studies of GaAs-AIxGal_xAs SL- structures of this kind and those modified by thick barriers between the EW and the SL regions [ 8 ] . Furthermore, a sin91e SL grown under the same conditions is studied to 9et information on recombination processes in the SL regions of the above-mentioned structures.
repetition rate of mode-locked cw-lasers [10]. It combines very high sensitivity, intermediate time resolution and a very simple realization. The kinetics of the SL- and EW-luminescence are measured in a temperature ran9e from 80 to 300 K usin 9 excitation by a mode-locked Ar + laser (514.5 nm). The luminescence is spectrally decomposed by interference filters and detected by a Si avalanche photodiode (APD: SP 114). The time resolution is achieved by modulatin 9 the 9ain of the avalanche diode with very short electrical pulses (200 ps). These pulses are formed by a reference APD from a small part of the laser output. The delay of the electrical pulses with respect to the excitation pulses can be scanned by a computer controlled optical delay line. Due to the high quantum efficiency of Si photodiodes the sensitivity of this electro-optical cross-correlation technique is comparable to that of time correlated sin91e photon
2. Experimental All samples investigated are nominally undoped SL grown by molecular-beam epitaxy. The thickness of the GaAs wells (Iw=3 nm) is chosen equal to that of the AIxGal_xAs barriers IB (x=0.35). The single SL consists of about 50 periods and is sandwiched between 200 nm AIxGal_xAs cladding layers to avoid carrier leaka9e. In the second sample a sin91e GaAs well in the middle of 52 SL-periods is enlar9ed to IEW =13.5 nm, whereas in the third sample the central GaAs well and the neighbour barriers are enlarged (IEW =IEB =13.5 nm). %
Mostly, mode-locked cw-lasers are used as the excitation source in ps-tuminescence experiments. Their high repetition rate in the order of 108 Hz allows for application of averagin9 techniques in different detection systems like time-correlated single photon counting [9], synchroscan streak camera E2], and frequency up-conversion technique E5]. We have used an electro-optical crosscorrelation technique especially desi9ned for the high
0749-6036/91/040503+04
S02 0 0 / 0
I
t [ns] Fig.1 Decay curves of the photoluminescence of the single superlattice measured at the peak position (;k=750 nm) for different mean excitation intensities, Dashed line: Measurement of the excitation pulse
© 1991 Academic Press Limited
Super/attices and Microstructures, Vol. 9, No. 4, 1991
504 countin 9 usin 9 photomultipliers with $1 or $25 cathode in the spectral range under consideration. By means of standard deconvulation methods [93 a time resolution of some ten ps is achieved. The mean excitation intensity is varied between 10 and about 300 W / c m 2 yieldin 9 carrier densities clearly above the residual dopin 9 of the samples.
3.Results In Fi9. 1 the decay curves measured on the short-period SL are given for various values of the mean excitation intensity Io. For comparison, the cross-correlation of the excitation pulse is drawn by a dashed line. The halfwidth of the pulse (FWHM) is about 300 ps. The oscillations found especially for negative delay are due to the electrical connections between reference diode and detectin 9 diode. In principle, they can be depressed by an improved electrical arran9ement [10], but, on the other hand, these oscillations make a more precise deconvolution possible. For the SL the decay is not simply exponential. For simplicity, we have defined the respective time constant at the 1/e-point, which increases from 2.2 ns up to 5.1 ns increasin 9 the excitation intensity by a factor of 30. Furthermore the time-inte9rated luminescence intensity shows a superlinear dependence on IO with an exponent of 1.6. These results can be well understand if we assume a dominatin 9 nonradiative recombination in the SL, where the nonradiative parallel channel tends to saturate with increasin 9 excitation intensity. Figs. 2 and 3 present the decay curves of SL- and EW-photoluminescence of the sample with enlarged well for 79 and 298 K, respectively. For the luminescence at the spectral position of the enlarged well practically no intensity dependence of the decay time is found, whereas the decay kinetics of the very weak SL-photoluminescence could be measured only at the hi9hest excitation intensity used. At 79 K a very fast decay of the $L- luminescence is observed with a time constant of about 20 ps. 1) This speed-up relative to pure SL has to be attributed to the capture of photoexcited electrons and holes into the enlar9ed well. At room temperature (Fi9. 3) the transport of the carriers is much slower which results in a considerably longer decay time of the SL luminescence of 210 ps.
I"
o i
;
'
4
'
t[ns]
Fi 9. 2 Decay curves of the EW- (811 nm) and SLluminescence (745 nm) measured on the superlattice with enlar9ed well at 79 K
298 K 310Wlcm 2
>,
i
0
'
{
'
t [ns]
Fig. 3 Decay curves of the EW- (854 nm) and SLluminescence (774 nm) at room temperature for the same sample as in Fi 9. 2.
I
?g K
230 W/cn~
c c
The decay curves of the luminescence from the enlar9ed well can be well fitted assumin 9 sin91e exponential decay. At 79 K a time constant of 700 ps is found, which increases at higher temperatures (950 ps at 120 K) and then drops down to 330 ps at room temperature (Fi9. 3). The latter is accompanied by a drastic reduction of the quantum yield. Whereas the first increase of life time with tile temperature corresponds to the known 1/T behaviour in a nonde9enerate two-dimensional electron-hole 9as, the drop down at hi9her temperatures might be attributed to a nonradiative recombination channel with a certain activation energy. Entirely, a similar dependence of the EWcarrier life time on temperature was observed in timeresolved photoluminescence studies on multiple-quantumwell structures [11].
1) This value and all followin 9 time constants are obtained by a deconvolution of the experimental curves.
I
'
t Ins]
I
4 -
Fig. 4 Decay curves of the EW- (808 nm) and SLluminescence (740 nm) at 79 K for the sample with enlar9ed well and enlar9ed barrrier.
The results obtained on the sample with an enlarged well separated by thick barriers from the SL are plotted in Figs. 4 and 5 for 79 K and 298 K, respectively. Comparing Figs. 2 and 4 the influence of the thick barriers on
Superlattices and Microstructures, VoL 9, No. 4, 1991
>
505
nlz.O)
~'VV~
298 K
I/~_~
240 W/cn~
~
Eclz) -7 E,(z) ~
F-l
SL
',EW
a
0
2
t[ns]
4
-
b c
SL Z ~
cl
Fig. 6 Schematic representation of z-dependence of conduction and valence band in the superlattice with enlar9ed well. The initially created distribution of carriers in the SL-regions is given by dashed areas.
Fi9. 5 Decay curves of the EW- (858 nm) and SLluminescence ( 773 nm) at room temperature for the same sample as in Fi 9. 4. r)~= Damb c)2n c~t -3z2 the capture of carriers into the EW is clearly seen. Here, the decay time of SL-luminescence (150 ps) is mainly determined by the tunnelin 9 of the carriers throu9h the enlarged barriers. At room temperature this time is further increased (200 ps), which indicates the additional influence of slower transport through the SL. At 79 K the decay time of the photoluminescence f r o m the EW is comparable to that of the sample without thick barriers, but no essential chan9e is observed when the temperature is increased up to 30OK. Correspondingly, the decrease of quantum yield with increasin 9 temperature is much less than that for the sample without thick barriers. The reason for this somewhat surprisin 9 different behaviour is not clear at present and needs further investi9ation. It looks like a suppression of the nonradiative recombination in the EW at room temperature by the enlarged barriers. 4. D i s c u s s i o n We have observed the transfer of photo-excited carriers from the SL to EW by a dramatic shortening of photoluminescence decay (see Fi 9. 2). For the transport of carriers throu9h the superlattice three different situations can be distinquished [ 6 ] : (i) The mean free path of the carriers is large compared to the extent of the SL. Then the coherence of the wave function is maintained over the whole structure and the transfer time is small compared to the collision time of the carriers (typically less than 1 ps). (ii) The mean free path is lar9e compared to the period of the SL, but clearly smaller than its extent. In this case the transport is diffusion-like through extended miniband states of the SL. (iii) If the mean free path of the carriers is smaller than the SL-period hopping transport has to taken into account. Our data suggest that the transfer of carriers to the EW is diffusion-like (ii). Since the excited carrier density is clearly above the residual doping of the samples we are faced with ambipolar diffusion.The corresponding diffusion constant can be obtained from the decay time of SLluminescence by solvin 9 the diffusion equation for both SL-re9ions of the sample (see Fi9. 6):
n tSL '
(1)
where tSL is the carrier life time in the SL. The boundary conditions read: z = a, d:
r)n/az = 0
(2)
z = b, c:
n = 0
(3)
The neglection of surface recombination at both ends of the structure is justified by the cladding layers used, whereas the assumption of an infinitely high trappin 9 rate at the interfaces to the EW in (3) accounts for the capture of carriers by the EW [12] which is much f a s t e r than the times typical for the transport through the SLregions and the time resolution available. The initial distribution is given by: n(z,O) = ~ N e x p ( - c c z )
(4)
where c~ is the absorption coefficient and N the number of photons of a S-like excitation pulse normalized per unit area. The small differences of c~ at the excitation wavelength in the SLand EW are neglected in (4). The initial distribution is visualized in Fig. 6 by dashed areas. The solution of the diffusion equation under the giver conditions is standard and can be expressed by: co
i
n(z,t) : : ~ [AkCOS~.kZ k=l
+ Bksin).kZ]
t (5)
exp(-t/zk/
,
where X k = (2k+l)~/(21SL) and 1/~ k = 1/I:sL + X 2 D, ISL= b-a = d-c is the len9th of each SL-region. Accordin 9 to (2) and (3) the Bl~s vanish for the left SL-re9ion, whereas the coefficients A k has to be determined f r o m the initial condition (4). For the right hand side SL-region the opposite situation holds. In the present model (1), that means dominating linear recombination, the luminescence intensity is proportional to the integrated population of the SL. For the given geometry (IsL =156 nm) and an absorption coefficient of 0¢ = 2 x l O - 4 c m -1 we have calculated numerically the time ~eff at which the initially created total population drops down to l / e , The results are given in Fig. 7 for different
Superlattices and Microstructures, VoL 9, No. 4, 1991
506
~1031"~=
of the enlarged barriers used here. Due to the different masses and band offsets the transition probability will be different for electrons, heavy holes and ligth holes. Nevertheless, the tunneling of only one kind of char9ed carriers will create an electric field which drastically increases the transition probability for the opposite charged one. Furthermore, in our experiments the tunneling start~ from extended miniband states of a superlattice and not from the discrete level of a quantum well as in [3,4]. In a first step, we will treat the reduced capture of carriers into the EW by taking into account a finite trapping rate in ( 3 )
5 ns
"-\
!
1 .....- : : t \
I
101~-, 0.1
, 1
\i D [cmZ/s]
10
Acknowledgement: We thank V. Jun9nicket for numerical treating the diffusion equation.
Fig. 7 Calculated decay time tel f of the SL-photoluminescence versus diffusion constant for different carrier life times tSL of the superlattice.
References carrier life times. Takin 9 tSL > 1 ns (Fig.l) we get from the decay times of the SL-luminescence in Figs. 2 and 3 the diffusion constant of Damb = 4.5 cm2/s and 0.3 cm2/s at 79 K and room temperature, respectively. For ambipolar transport Darnb = 2D h holds since the diffusion constant of the electrons is much lar9er than that of the holes in these material. The resultin 9 value of Dh = 2.3 cm2/s agrees fairly well with that of AIxGal_xAs mixed crystals with equivalent admixture x = 0.15 (Dh 3 cm2/s at 140 K [12]). That proves that indeed diffusionlike ambipolar transport takes place through the extended states of the SL with a period d = Iw + IB = 6 nm. On the other hand, such value of period will be an upper limit for this kind of hole transport. A remarkable reduction of the Dh compared to the alloy value is already found for such SL-period in similar experiments [12]. The smaller value of Dh at room temperature indicates the 9rowin9 influence of phonon scatterin 9 on the mobility of the carriers in the SL at hi9her temperatures. The interestin 9 comparison with the values for an equivalent alloy is not possible at the moment due to the lack of data. The separation of the EW from the SL by enlar9ed barriers leads indeed to a reduced capture of carriers by the EW (Fi9s. 4 and 5). At 79 K the observed decay time of the SL-luminescence of 150 ps should be determined by the finite transition probability of electrons and holes throu9h the enlarged barriers. Compared to the time constants observed in nonresonant tunnelin 9 between asymmetric quantum wells [3,4] the above value seems to be rather small takin 9 into account the larger thickness
[I] J. Shah, Superlattices and Microstructures 6, 293 (1989). [2] W. W. RUhle, K. Leo and E Bauser, Phys. Rev. B 40, 1756 (1989). [ 3 ] D. Y. Oberli, J. Shah, T. C. Damen, J. M. Kuo, J. E. Henry, J. Lary and St. M. Goodnick, Appl. Phys. Lett. 56, 1239 (1990). [ 4 ] U. Nido, M. G. W. Alexander, W. W. RUhle, T. Schweitzer and K. K~hler, Appl. Phys. Lett. 56, 355 (1990). [ 5 ] U. Cebulla, G. Bacher, A. Forchel, D. Schmitz, H. JUr9ensen and M. Razeghi, Appl. Phys. Lett. 55, 933 (1989). [ 6 ] B. Deveaud, J. Shah, T. C. Damen, 8. Lambert, A. Chomette and A. Regreny, IEEE J. Quant. Electronics 24, 1641 (1988). [7] A. Chomette, B. Deveaud, J. Y. Emery, A. Re9reny and B. Lambert, Solid State Commun. 54, 75 (1985). K. Fujiwara, J. L deMi9uet and K. Ploo9, Japan. J. Appl. Phys. 24, L405 (1985). [8] J. Puls, F. Henneberger , I. N. Uraltsev, A. M. Vasiliev, U. Wo99on and M. Luhn, Proc. Internat. Syrup. "Ultrafast Penomena in Spectroscopy", Neubrandenbur9 (GDR), 1989 (to be published). [ 9 ] D. V. O'Connor and D. Phillips, "Time-Correlated Sin91e Photon Countin9", Academic Press, London 1984. [10] K. Berndt, Optics Commun. 61, 33 (1987). [11] T. Miyoshi, Y. Aoyagi , Y. Segawa and S. Namba, Japan. J. Appl. Phys. 24, 369 (1985). [12] B. Lambert, F. Clerot, B. Deveaud, A. Chomette, G. Talalaeff, A. Re9reny and B. Sermage , J. Luminescence 44, 277 (1989).
503
PICOSECOND LUMINESCENCE STUDIES OF VERTICAL TRANSPORT IN SHORT-PERIOD SUPERLATTICES J. Puls (a), F. Henneber9er [a), I. N. Uraltsev (b), and A. M. Vaslllev (b] (a) H u m b o l d t - U n i v e r s i t y , D e p a r t m e n t of Physics, I n v a l i d e n s t r . 110, 1040 Berlin, GDR, and (b) A. F. I of f e P h y s i c o - T e c h n i c a l I n s t i t u t e , Academy of Sciences, 194021 L e n i n 9 r a d , USSR (Received 13 August 1990)
Photoluminescence studies with ps-time resolution are reported for three different types of GaAs-AIGaAs microstructures: (i) a short-period superlattice, (ii) a superlattice, where an enlarged well is introduced into the center, and, (iii) a superlattice, where this well is separated from the superlattice by enlar9ed barriers. Ex~:itin9 the samples by a mode-locked Ar + laser very high sensitivity is achieved by an electrooptical cross-correlation technique usin 9 a 9ain modulated Si avalanche photodiode as a detector. From the data obtained we are able to determine the relevant parameters of vertical transport and nonradiative recombination in the respective structures.
1. Introduction Time-resolved photoluminescence experiments are a powerful tool to study different aspects of carrier kinetics in semiconductor microstructures like e. 9, carrier relaxation [1,23, tunnelin 9 between coupled quantum wells [3,4], capture of carriers into the quantum well E53, and their transport perpendicular to the layers of a superlattice (SL) [6]. In the latter case, usually, an enlarged well (EW) is incorporated into the SL [7] to detect the arrival of the photo-excited carriers at the position of the EW. Here, we report on comparative studies of GaAs-AIxGal_xAs SL- structures of this kind and those modified by thick barriers between the EW and the SL regions [ 8 ] . Furthermore, a sin91e SL grown under the same conditions is studied to 9et information on recombination processes in the SL regions of the above-mentioned structures.
repetition rate of mode-locked cw-lasers [10]. It combines very high sensitivity, intermediate time resolution and a very simple realization. The kinetics of the SL- and EW-luminescence are measured in a temperature ran9e from 80 to 300 K usin 9 excitation by a mode-locked Ar + laser (514.5 nm). The luminescence is spectrally decomposed by interference filters and detected by a Si avalanche photodiode (APD: SP 114). The time resolution is achieved by modulatin 9 the 9ain of the avalanche diode with very short electrical pulses (200 ps). These pulses are formed by a reference APD from a small part of the laser output. The delay of the electrical pulses with respect to the excitation pulses can be scanned by a computer controlled optical delay line. Due to the high quantum efficiency of Si photodiodes the sensitivity of this electro-optical cross-correlation technique is comparable to that of time correlated sin91e photon
2. Experimental All samples investigated are nominally undoped SL grown by molecular-beam epitaxy. The thickness of the GaAs wells (Iw=3 nm) is chosen equal to that of the AIxGal_xAs barriers IB (x=0.35). The single SL consists of about 50 periods and is sandwiched between 200 nm AIxGal_xAs cladding layers to avoid carrier leaka9e. In the second sample a sin91e GaAs well in the middle of 52 SL-periods is enlar9ed to IEW =13.5 nm, whereas in the third sample the central GaAs well and the neighbour barriers are enlarged (IEW =IEB =13.5 nm). %
Mostly, mode-locked cw-lasers are used as the excitation source in ps-tuminescence experiments. Their high repetition rate in the order of 108 Hz allows for application of averagin9 techniques in different detection systems like time-correlated single photon counting [9], synchroscan streak camera E2], and frequency up-conversion technique E5]. We have used an electro-optical crosscorrelation technique especially desi9ned for the high
0749-6036/91/040503+04
S02 0 0 / 0
I
t [ns] Fig.1 Decay curves of the photoluminescence of the single superlattice measured at the peak position (;k=750 nm) for different mean excitation intensities, Dashed line: Measurement of the excitation pulse
© 1991 Academic Press Limited
Super/attices and Microstructures, Vol. 9, No. 4, 1991
504 countin 9 usin 9 photomultipliers with $1 or $25 cathode in the spectral range under consideration. By means of standard deconvulation methods [93 a time resolution of some ten ps is achieved. The mean excitation intensity is varied between 10 and about 300 W / c m 2 yieldin 9 carrier densities clearly above the residual dopin 9 of the samples.
3.Results In Fi9. 1 the decay curves measured on the short-period SL are given for various values of the mean excitation intensity Io. For comparison, the cross-correlation of the excitation pulse is drawn by a dashed line. The halfwidth of the pulse (FWHM) is about 300 ps. The oscillations found especially for negative delay are due to the electrical connections between reference diode and detectin 9 diode. In principle, they can be depressed by an improved electrical arran9ement [10], but, on the other hand, these oscillations make a more precise deconvolution possible. For the SL the decay is not simply exponential. For simplicity, we have defined the respective time constant at the 1/e-point, which increases from 2.2 ns up to 5.1 ns increasin 9 the excitation intensity by a factor of 30. Furthermore the time-inte9rated luminescence intensity shows a superlinear dependence on IO with an exponent of 1.6. These results can be well understand if we assume a dominatin 9 nonradiative recombination in the SL, where the nonradiative parallel channel tends to saturate with increasin 9 excitation intensity. Figs. 2 and 3 present the decay curves of SL- and EW-photoluminescence of the sample with enlarged well for 79 and 298 K, respectively. For the luminescence at the spectral position of the enlarged well practically no intensity dependence of the decay time is found, whereas the decay kinetics of the very weak SL-photoluminescence could be measured only at the hi9hest excitation intensity used. At 79 K a very fast decay of the $L- luminescence is observed with a time constant of about 20 ps. 1) This speed-up relative to pure SL has to be attributed to the capture of photoexcited electrons and holes into the enlar9ed well. At room temperature (Fi9. 3) the transport of the carriers is much slower which results in a considerably longer decay time of the SL luminescence of 210 ps.
I"
o i
;
'
4
'
t[ns]
Fi 9. 2 Decay curves of the EW- (811 nm) and SLluminescence (745 nm) measured on the superlattice with enlar9ed well at 79 K
298 K 310Wlcm 2
>,
i
0
'
{
'
t [ns]
Fig. 3 Decay curves of the EW- (854 nm) and SLluminescence (774 nm) at room temperature for the same sample as in Fi 9. 2.
I
?g K
230 W/cn~
c c
The decay curves of the luminescence from the enlar9ed well can be well fitted assumin 9 sin91e exponential decay. At 79 K a time constant of 700 ps is found, which increases at higher temperatures (950 ps at 120 K) and then drops down to 330 ps at room temperature (Fi9. 3). The latter is accompanied by a drastic reduction of the quantum yield. Whereas the first increase of life time with tile temperature corresponds to the known 1/T behaviour in a nonde9enerate two-dimensional electron-hole 9as, the drop down at hi9her temperatures might be attributed to a nonradiative recombination channel with a certain activation energy. Entirely, a similar dependence of the EWcarrier life time on temperature was observed in timeresolved photoluminescence studies on multiple-quantumwell structures [11].
1) This value and all followin 9 time constants are obtained by a deconvolution of the experimental curves.
I
'
t Ins]
I
4 -
Fig. 4 Decay curves of the EW- (808 nm) and SLluminescence (740 nm) at 79 K for the sample with enlar9ed well and enlar9ed barrrier.
The results obtained on the sample with an enlarged well separated by thick barriers from the SL are plotted in Figs. 4 and 5 for 79 K and 298 K, respectively. Comparing Figs. 2 and 4 the influence of the thick barriers on
Superlattices and Microstructures, VoL 9, No. 4, 1991
>
505
nlz.O)
~'VV~
298 K
I/~_~
240 W/cn~
~
Eclz) -7 E,(z) ~
F-l
SL
',EW
a
0
2
t[ns]
4
-
b c
SL Z ~
cl
Fig. 6 Schematic representation of z-dependence of conduction and valence band in the superlattice with enlar9ed well. The initially created distribution of carriers in the SL-regions is given by dashed areas.
Fi9. 5 Decay curves of the EW- (858 nm) and SLluminescence ( 773 nm) at room temperature for the same sample as in Fi 9. 4. r)~= Damb c)2n c~t -3z2 the capture of carriers into the EW is clearly seen. Here, the decay time of SL-luminescence (150 ps) is mainly determined by the tunnelin 9 of the carriers throu9h the enlarged barriers. At room temperature this time is further increased (200 ps), which indicates the additional influence of slower transport through the SL. At 79 K the decay time of the photoluminescence f r o m the EW is comparable to that of the sample without thick barriers, but no essential chan9e is observed when the temperature is increased up to 30OK. Correspondingly, the decrease of quantum yield with increasin 9 temperature is much less than that for the sample without thick barriers. The reason for this somewhat surprisin 9 different behaviour is not clear at present and needs further investi9ation. It looks like a suppression of the nonradiative recombination in the EW at room temperature by the enlarged barriers. 4. D i s c u s s i o n We have observed the transfer of photo-excited carriers from the SL to EW by a dramatic shortening of photoluminescence decay (see Fi 9. 2). For the transport of carriers throu9h the superlattice three different situations can be distinquished [ 6 ] : (i) The mean free path of the carriers is large compared to the extent of the SL. Then the coherence of the wave function is maintained over the whole structure and the transfer time is small compared to the collision time of the carriers (typically less than 1 ps). (ii) The mean free path is lar9e compared to the period of the SL, but clearly smaller than its extent. In this case the transport is diffusion-like through extended miniband states of the SL. (iii) If the mean free path of the carriers is smaller than the SL-period hopping transport has to taken into account. Our data suggest that the transfer of carriers to the EW is diffusion-like (ii). Since the excited carrier density is clearly above the residual doping of the samples we are faced with ambipolar diffusion.The corresponding diffusion constant can be obtained from the decay time of SLluminescence by solvin 9 the diffusion equation for both SL-re9ions of the sample (see Fi9. 6):
n tSL '
(1)
where tSL is the carrier life time in the SL. The boundary conditions read: z = a, d:
r)n/az = 0
(2)
z = b, c:
n = 0
(3)
The neglection of surface recombination at both ends of the structure is justified by the cladding layers used, whereas the assumption of an infinitely high trappin 9 rate at the interfaces to the EW in (3) accounts for the capture of carriers by the EW [12] which is much f a s t e r than the times typical for the transport through the SLregions and the time resolution available. The initial distribution is given by: n(z,O) = ~ N e x p ( - c c z )
(4)
where c~ is the absorption coefficient and N the number of photons of a S-like excitation pulse normalized per unit area. The small differences of c~ at the excitation wavelength in the SLand EW are neglected in (4). The initial distribution is visualized in Fig. 6 by dashed areas. The solution of the diffusion equation under the giver conditions is standard and can be expressed by: co
i
n(z,t) : : ~ [AkCOS~.kZ k=l
+ Bksin).kZ]
t (5)
exp(-t/zk/
,
where X k = (2k+l)~/(21SL) and 1/~ k = 1/I:sL + X 2 D, ISL= b-a = d-c is the len9th of each SL-region. Accordin 9 to (2) and (3) the Bl~s vanish for the left SL-re9ion, whereas the coefficients A k has to be determined f r o m the initial condition (4). For the right hand side SL-region the opposite situation holds. In the present model (1), that means dominating linear recombination, the luminescence intensity is proportional to the integrated population of the SL. For the given geometry (IsL =156 nm) and an absorption coefficient of 0¢ = 2 x l O - 4 c m -1 we have calculated numerically the time ~eff at which the initially created total population drops down to l / e , The results are given in Fig. 7 for different
Superlattices and Microstructures, VoL 9, No. 4, 1991
506
~1031"~=
of the enlarged barriers used here. Due to the different masses and band offsets the transition probability will be different for electrons, heavy holes and ligth holes. Nevertheless, the tunneling of only one kind of char9ed carriers will create an electric field which drastically increases the transition probability for the opposite charged one. Furthermore, in our experiments the tunneling start~ from extended miniband states of a superlattice and not from the discrete level of a quantum well as in [3,4]. In a first step, we will treat the reduced capture of carriers into the EW by taking into account a finite trapping rate in ( 3 )
5 ns
"-\
!
1 .....- : : t \
I
101~-, 0.1
, 1
\i D [cmZ/s]
10
Acknowledgement: We thank V. Jun9nicket for numerical treating the diffusion equation.
Fig. 7 Calculated decay time tel f of the SL-photoluminescence versus diffusion constant for different carrier life times tSL of the superlattice.
References carrier life times. Takin 9 tSL > 1 ns (Fig.l) we get from the decay times of the SL-luminescence in Figs. 2 and 3 the diffusion constant of Damb = 4.5 cm2/s and 0.3 cm2/s at 79 K and room temperature, respectively. For ambipolar transport Darnb = 2D h holds since the diffusion constant of the electrons is much lar9er than that of the holes in these material. The resultin 9 value of Dh = 2.3 cm2/s agrees fairly well with that of AIxGal_xAs mixed crystals with equivalent admixture x = 0.15 (Dh 3 cm2/s at 140 K [12]). That proves that indeed diffusionlike ambipolar transport takes place through the extended states of the SL with a period d = Iw + IB = 6 nm. On the other hand, such value of period will be an upper limit for this kind of hole transport. A remarkable reduction of the Dh compared to the alloy value is already found for such SL-period in similar experiments [12]. The smaller value of Dh at room temperature indicates the 9rowin9 influence of phonon scatterin 9 on the mobility of the carriers in the SL at hi9her temperatures. The interestin 9 comparison with the values for an equivalent alloy is not possible at the moment due to the lack of data. The separation of the EW from the SL by enlar9ed barriers leads indeed to a reduced capture of carriers by the EW (Fi9s. 4 and 5). At 79 K the observed decay time of the SL-luminescence of 150 ps should be determined by the finite transition probability of electrons and holes throu9h the enlarged barriers. Compared to the time constants observed in nonresonant tunnelin 9 between asymmetric quantum wells [3,4] the above value seems to be rather small takin 9 into account the larger thickness
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