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GaAs system by quantum oscillations of photoluminescence intensity
Surface Science 174 (1986) 307-311 North-Holland, Amsterdam
307
DETERMINATION OF BAND-GAP DISCONTINUITY IN AlGaAs/GaAs SYSTEM BY QUANTUM OSCILLATIONS OF PHOTOLUMINESCENCE IN~NS~ T. MISHIMA, J. KASAI, and Y. SHIRAKI
M. MORIOKA,
Y. SAWADA,
Y. KATAYAMA
Cenrrai Research Laboratmy, Hitachi, Lrd., Kokubunji, Tokyo 18.5,Japan and Y. MURAYAMA Aduanced Research Laboratory, Hitachi, Ltd., Kokubunji, Tokyo I85, Japan Received
29 July 1985; accepted
for publication
15 November
1985
An anomalous excitation intensity dependence of photoluminescence (PL) in high-quality Al,,Ga, ,As/GaAs quantum wells was observed at low temperatures. The PL intensity I,, was seen to increase as Z,, a Z& with increasing excitation intensity ZEX and the power m varied periodically between 1 and 2, depending on the well width. This phenomenon can be understood in terms of the carrier trapping efficiency under resonant and off-resonant conditions. From the theoretical analysis of the effect, the conduction band off-set can be estimated to be 59-708, considerably smaller than the value of Dingle et al.
1. Introduction A great deal of discussion has taken place on the band-gap discontinuity in the AlGaAs/GaAs system, which is one of the most fundamental values in the design of heterostructure devices. Since the report of the 85% rule [ll, several recent studies have claimed smaller values [2-41. In this paper an excitation dependence of PL in the same quantum wells (QWs) with various well widths is described. A preliminary theoretical analysis justifies and reproduces the periodic variation of the PL, from whose critical values the band-gap discontinuity is determined.
2. Experiment A typical QW wafer consists of six GaAs wells with a series of widths, 15-155 A, each separated from the others by a 500 A thick Al,,,Ga,,,As 0039-6028/86/$03.50 Physics Publishing
0 Elsevier Science Publishers B.V. (North-Holland Division) and Yamada Science Foundation
T. Mishima et al. / Band-gap discontmult~
30x
MIAIGuAs/GaAs
barrier. The QW wafers were prepared by molecular beam epitaxy (MBE) using a specially purified Al source. All the wells showed very sharp PL spectra (FWHM = 1.1 meV for Lz = 155 A, x = 0.3 at T= 77 K). that indicate formation of high-quality AlGaAs/GaAs interfaces. PL measurements were performed at 77 K with excitation by an Ar+ laser (h = 4579-5145 A) whose intensity was varied from 0.05 to 1 W. The excited area was 0.016 mm’.
3. Results and discussion Fig. 1 shows typical PL spectra from the QWs at excitation intensities ZEx of (a) 600 mW and (b) 6 mW for X = 5145 A. At the low I,,. the decreases in I,, from alternate wells with Lz = 15, 47, and 94 A are remarkable in contrast to those from the others. Each detailed measurement of log I,, versus log I,, gives a constant m as a gradient (I,, a ZFx), as is plotted in fig. 2. The gradients for QWs with L, = 15, 47 and 94 A become larger than 1 in the decrease in lower excitation region (I,, ,< 0.1 W) resulting in a remarkable I rL. All the gradients become close to unity for all QWs in the higher excitation region (I,, > 0.1 W). The m values are plotted in fig. 3 as a function of the well width. They vary periodically between 1 and 2 as the well width is changed. At first, this I
I
I
I
28A
77K
47A
I
I
26 ii
15A
77K
ak./AI.,Ga.,As O”o”t”m
Well’
4,= 600 mW
66A
154 94A
I
%IA
4 ,,
1
800
750
WAVELENGTH
700
I(
I
Ii
-
65’0
15(
(nml
Fig. 1. Photoluminescence spectra of MBE-grown excitation intensities of (a) 600 mW and (b) 6 mW.
WAVELENGTH
AI ,,Ga,,As/GaAs
(nmi
QWs
at 77 K with
309
T. ~jshirna et al. / Band-gap discontinuity in AtGaAs/ GaAs
,’ / I
9LA:6 :
GaAs/AI,,Ga,,As
1o-3
I 10-l
1O-2
EXCITATION
Fig. 2. Relationship the well width.
z -
I 1
INTENSITY
of PL intensity
(W 1
(I,,)
and excitation
intensity
(I,,)
;r
at 77 K. The parameter
i.6-
0
I
. 4-
A
1.2-
t
f
\;\
‘1
______-.o._---
. 0-
*
0
______-___________--
f
0.ai
0
*
2 *
‘
4*
*
6
WELL Fig. 3. Dependence
of m( I,,
’
’
a
is
)_ .
0
1.a-
w -
Wells
Quantum
i
I ’
x
: “
’
WIDTH
*
fO
(
12
nm
14
I
16
)
a I&) on well width. The solid line is the calculated
dependence.
T. Mishmzo
Ed
ul.
/
J
--N Well
Fig. 4. Graphic
explanation
Barrier of the model considered
in this study.
anomalous behavior was thought to come from optical interference within the QWs. However, no significant dependence of m on excitation wavelength from h = 4579 to 5145 A was observed. Moreover. samples with quite different total thicknesses, that is, those with 300 A thick barriers (A) and those with two quantum wells (EL!),both showed the same dependence as is seen in fig. 3. Thus we can infer that the phenomenon is not optical interference, but must be correlated to the basic electronic structure, The periodic variation suggests that relation of the highest QW level to the conduction band of the barrier is responsible for the phenomenon. When the band bottom of AlGaAs, which photoexcited electrons occupy, is under resonant condition against the quantum level (i.e., both have the same energy). electrons stay within the well and the barrier as well; this indicates that they are erratic in their escapes from the well. On the other hand, when the condition is off-resonant, they are tightly trapped and destined to relax into the n = 1 state of the QW subband. This final state eventually causes radiative reconlbination (fig. 4). We analyzed two rate equations:
where n, and n,, stand for the densities of electrons in the well aud the barrier, respectively. The maximum densities of states that can accommodate electrons are denoted likewise by N, and N,. Since N,V is proportional to temperature, a strongly populated state is described by a hot electron temperature, which always causes IV,, - n, to be positive according to a larger IV,. P,, is the prabability of electron transfer from the barrier to the well. PC,+,is that for the reverse process. T,?, is the non-radiative relaxation time. while the last
T. Mishima et al. / Band-gap discontinuity in AlGaAs/GaAs
311
term in the second equation is the radiative rate of recombination with holes rate. which we assume linear to I,,. CX~,, is the electron generation From the rate equations, it is easy to show that m of I,, CCnwpw is 2 under resonance, while it is 1 far off-resonance, so long as the excitation level is low enough. As for the values in between, we must calculate microscopically the transition probability of the multiple phonon emission process as a function of the initial kinetic energy ck of an electron transferred from the barrier [5] (see fig. 4). In this model, a high-energy electron with ek larger than n times fiwor is forced to emit n optical phonons (multiple optical phonon emission). At the final stage of the relaxation, the electron with energy no longer sufficient to emit such a phonon is assumed to emit multiple acoustic phonons. The results are shown in fig. 3. It can also be shown that for larger 1,x the m = 2 state is difficult to realize even under the resonant condition. From the critical well width where the first resonance occurs, the conduction-band off-set can be estimated to be 59-70s. This ambiguity is the result of the lack of data points around the critical width. It should be noted that this effect is not clearly observed in samples with Al content of x = 0.5 for barriers. The difference seems ascribable to the fact that there the resonance transfer from barriers to wells is considerably suppressed because of the indirect feature of the transition.
p,,
4. Summary An anomalous excitation intensity dependence of PL in AlGaAs/GaAs QWs was observed for the first time. This anomalous effect gives us information on the resonance transfer of carriers from barrier band states to quantized 2D subbands. This mechanism provides us with a new method to obtain monochromatic hot carriers and a very powerful tool to study the relaxation scheme of non-equilibrium electrons. From the PL measurement, a rather small band off-set of 59-70% is concluded for electrons.
References [l] [2] [3] f4]
R. Dingle, W. Wiegmann and C.H. Henry, Phys. Rev. Letters 33 (1974) 827. H. Kroemer, W.Y. Chien, J.S. Harris, Jr., and D.D. Edwall. Appt. Phys. Letters 36 (1980) 295. R.C. Miller, D.A. Gossard, D.A. Kleinmann and 0. Munteanu, Phys. Rev. B29 (1984) 3740. D. Arnold, A. Ketterson, T. Henderson, J. Klem and H. Morkos, J. Appl. Phys. 57 (1985) 2880. [5] Y. Murayama, Appl. Phys., to be published.
307
DETERMINATION OF BAND-GAP DISCONTINUITY IN AlGaAs/GaAs SYSTEM BY QUANTUM OSCILLATIONS OF PHOTOLUMINESCENCE IN~NS~ T. MISHIMA, J. KASAI, and Y. SHIRAKI
M. MORIOKA,
Y. SAWADA,
Y. KATAYAMA
Cenrrai Research Laboratmy, Hitachi, Lrd., Kokubunji, Tokyo 18.5,Japan and Y. MURAYAMA Aduanced Research Laboratory, Hitachi, Ltd., Kokubunji, Tokyo I85, Japan Received
29 July 1985; accepted
for publication
15 November
1985
An anomalous excitation intensity dependence of photoluminescence (PL) in high-quality Al,,Ga, ,As/GaAs quantum wells was observed at low temperatures. The PL intensity I,, was seen to increase as Z,, a Z& with increasing excitation intensity ZEX and the power m varied periodically between 1 and 2, depending on the well width. This phenomenon can be understood in terms of the carrier trapping efficiency under resonant and off-resonant conditions. From the theoretical analysis of the effect, the conduction band off-set can be estimated to be 59-708, considerably smaller than the value of Dingle et al.
1. Introduction A great deal of discussion has taken place on the band-gap discontinuity in the AlGaAs/GaAs system, which is one of the most fundamental values in the design of heterostructure devices. Since the report of the 85% rule [ll, several recent studies have claimed smaller values [2-41. In this paper an excitation dependence of PL in the same quantum wells (QWs) with various well widths is described. A preliminary theoretical analysis justifies and reproduces the periodic variation of the PL, from whose critical values the band-gap discontinuity is determined.
2. Experiment A typical QW wafer consists of six GaAs wells with a series of widths, 15-155 A, each separated from the others by a 500 A thick Al,,,Ga,,,As 0039-6028/86/$03.50 Physics Publishing
0 Elsevier Science Publishers B.V. (North-Holland Division) and Yamada Science Foundation
T. Mishima et al. / Band-gap discontmult~
30x
MIAIGuAs/GaAs
barrier. The QW wafers were prepared by molecular beam epitaxy (MBE) using a specially purified Al source. All the wells showed very sharp PL spectra (FWHM = 1.1 meV for Lz = 155 A, x = 0.3 at T= 77 K). that indicate formation of high-quality AlGaAs/GaAs interfaces. PL measurements were performed at 77 K with excitation by an Ar+ laser (h = 4579-5145 A) whose intensity was varied from 0.05 to 1 W. The excited area was 0.016 mm’.
3. Results and discussion Fig. 1 shows typical PL spectra from the QWs at excitation intensities ZEx of (a) 600 mW and (b) 6 mW for X = 5145 A. At the low I,,. the decreases in I,, from alternate wells with Lz = 15, 47, and 94 A are remarkable in contrast to those from the others. Each detailed measurement of log I,, versus log I,, gives a constant m as a gradient (I,, a ZFx), as is plotted in fig. 2. The gradients for QWs with L, = 15, 47 and 94 A become larger than 1 in the decrease in lower excitation region (I,, ,< 0.1 W) resulting in a remarkable I rL. All the gradients become close to unity for all QWs in the higher excitation region (I,, > 0.1 W). The m values are plotted in fig. 3 as a function of the well width. They vary periodically between 1 and 2 as the well width is changed. At first, this I
I
I
I
28A
77K
47A
I
I
26 ii
15A
77K
ak./AI.,Ga.,As O”o”t”m
Well’
4,= 600 mW
66A
154 94A
I
%IA
4 ,,
1
800
750
WAVELENGTH
700
I(
I
Ii
-
65’0
15(
(nml
Fig. 1. Photoluminescence spectra of MBE-grown excitation intensities of (a) 600 mW and (b) 6 mW.
WAVELENGTH
AI ,,Ga,,As/GaAs
(nmi
QWs
at 77 K with
309
T. ~jshirna et al. / Band-gap discontinuity in AtGaAs/ GaAs
,’ / I
9LA:6 :
GaAs/AI,,Ga,,As
1o-3
I 10-l
1O-2
EXCITATION
Fig. 2. Relationship the well width.
z -
I 1
INTENSITY
of PL intensity
(W 1
(I,,)
and excitation
intensity
(I,,)
;r
at 77 K. The parameter
i.6-
0
I
. 4-
A
1.2-
t
f
\;\
‘1
______-.o._---
. 0-
*
0
______-___________--
f
0.ai
0
*
2 *
‘
4*
*
6
WELL Fig. 3. Dependence
of m( I,,
’
’
a
is
)_ .
0
1.a-
w -
Wells
Quantum
i
I ’
x
: “
’
WIDTH
*
fO
(
12
nm
14
I
16
)
a I&) on well width. The solid line is the calculated
dependence.
T. Mishmzo
Ed
ul.
/
J
--N Well
Fig. 4. Graphic
explanation
Barrier of the model considered
in this study.
anomalous behavior was thought to come from optical interference within the QWs. However, no significant dependence of m on excitation wavelength from h = 4579 to 5145 A was observed. Moreover. samples with quite different total thicknesses, that is, those with 300 A thick barriers (A) and those with two quantum wells (EL!),both showed the same dependence as is seen in fig. 3. Thus we can infer that the phenomenon is not optical interference, but must be correlated to the basic electronic structure, The periodic variation suggests that relation of the highest QW level to the conduction band of the barrier is responsible for the phenomenon. When the band bottom of AlGaAs, which photoexcited electrons occupy, is under resonant condition against the quantum level (i.e., both have the same energy). electrons stay within the well and the barrier as well; this indicates that they are erratic in their escapes from the well. On the other hand, when the condition is off-resonant, they are tightly trapped and destined to relax into the n = 1 state of the QW subband. This final state eventually causes radiative reconlbination (fig. 4). We analyzed two rate equations:
where n, and n,, stand for the densities of electrons in the well aud the barrier, respectively. The maximum densities of states that can accommodate electrons are denoted likewise by N, and N,. Since N,V is proportional to temperature, a strongly populated state is described by a hot electron temperature, which always causes IV,, - n, to be positive according to a larger IV,. P,, is the prabability of electron transfer from the barrier to the well. PC,+,is that for the reverse process. T,?, is the non-radiative relaxation time. while the last
T. Mishima et al. / Band-gap discontinuity in AlGaAs/GaAs
311
term in the second equation is the radiative rate of recombination with holes rate. which we assume linear to I,,. CX~,, is the electron generation From the rate equations, it is easy to show that m of I,, CCnwpw is 2 under resonance, while it is 1 far off-resonance, so long as the excitation level is low enough. As for the values in between, we must calculate microscopically the transition probability of the multiple phonon emission process as a function of the initial kinetic energy ck of an electron transferred from the barrier [5] (see fig. 4). In this model, a high-energy electron with ek larger than n times fiwor is forced to emit n optical phonons (multiple optical phonon emission). At the final stage of the relaxation, the electron with energy no longer sufficient to emit such a phonon is assumed to emit multiple acoustic phonons. The results are shown in fig. 3. It can also be shown that for larger 1,x the m = 2 state is difficult to realize even under the resonant condition. From the critical well width where the first resonance occurs, the conduction-band off-set can be estimated to be 59-70s. This ambiguity is the result of the lack of data points around the critical width. It should be noted that this effect is not clearly observed in samples with Al content of x = 0.5 for barriers. The difference seems ascribable to the fact that there the resonance transfer from barriers to wells is considerably suppressed because of the indirect feature of the transition.
p,,
4. Summary An anomalous excitation intensity dependence of PL in AlGaAs/GaAs QWs was observed for the first time. This anomalous effect gives us information on the resonance transfer of carriers from barrier band states to quantized 2D subbands. This mechanism provides us with a new method to obtain monochromatic hot carriers and a very powerful tool to study the relaxation scheme of non-equilibrium electrons. From the PL measurement, a rather small band off-set of 59-70% is concluded for electrons.
References [l] [2] [3] f4]
R. Dingle, W. Wiegmann and C.H. Henry, Phys. Rev. Letters 33 (1974) 827. H. Kroemer, W.Y. Chien, J.S. Harris, Jr., and D.D. Edwall. Appt. Phys. Letters 36 (1980) 295. R.C. Miller, D.A. Gossard, D.A. Kleinmann and 0. Munteanu, Phys. Rev. B29 (1984) 3740. D. Arnold, A. Ketterson, T. Henderson, J. Klem and H. Morkos, J. Appl. Phys. 57 (1985) 2880. [5] Y. Murayama, Appl. Phys., to be published.