- Email: [email protected]
GaAs quantum well structures
Surface
Science
263 (1902) 642-645
surface science ::: ..:,.,’ ; : ,,,.. :“.
North-Holland
Observation of resonant well structures
WC dcmonstratc well\.
The sample
cat reflectivity quantized
for
of the electron.
time thin
efficiency
the lurrier
quantized
under
band-edge
tunnel
that the capture
dependent condition
capture
evidence
harriers
is ascribed
in AlGaAs/GaAs
tar the resonant
ckctl-on
on both 5idcs of the C;aAs well efficiency
on the well width
state in the well coincide\
the resonant
is found
the experrmenM
AlAs
It was found
state of the well is strongly
is such that the highest capture
the first
used contains
electron
with
of photogenerated
nnd increnw
under
the concluction-hnr,d
to the incread
capture
quantum
111AI<;~A\;C~:IA\
layer to cnhancc electrons
the resonant
in the r\lC;:tAs condition
edge ot the AIC;aA\
proluhility
that the clcctron
qu;~n~um
the qu~rntun~-rn~cli~~~~iwhere barr-icr.
harrier
into the
the well width The cnh;lnced
in the continuum
\t;ltt’
;~i
in the wcII
The capture of electrons and holes into ;I quantum well (QW) has ken attracting considerable intcrcst in terms of the device application and the underlying physical mechanism. The mechanism of carrier capture has been theoretically investigated from a quantum mechanical point of view 1121. Especially, the capture efficiency is expected to bc dependent on the well width and be enhanced under the resonant condition where the band-edge energy of the barrier is nearly equal to the highest QW level [I]. This resonant effect can bc understood by regarding a QW as a Fabry-Perot resonator of the incident electron wave in the barrier and are due to the interference of the coherent electron wave. Under the resonant condition, the wavefunction 01 incoming electrons from the barrier band-edge significantly accumulates in the well compared with the off-resonant condition. This is thought to lead to an increased capture efficiency. However. no experimental evidence of this effect has been presented so far [S-S]. In this paper, we report the first observation of the clcctron resonant capture in specially designed AlGaAs/GaAs QW
structures by means 01‘ photoluminescence (PL). It is demonstrated that the capture efficiency in a QW is dependent on the well width and is drastically enhanced under the resonant condition. The samples used wcrc grown by molecular beam cpitaxy (MBE) on semi-insulating GaAs (100) substrates. The band diagram of the htI-uclure is schematically illustrated in fig. I. .l‘he prominent feature is that thin AlAs tunnel harri-
GaAs oAI,Go,
7508
643
A. F~j~wa~a et al. / ~bser~~~t~~~ of remnant electron capture in AlGaAs / GaAs Q W st~~i~res
ers of 20 A are symmetrically inserted at heterointerfaces of the Al,,,Ga,.,As/GaAs QW structure and the QW structure is clad by AlAs layers to prevent carrier overflow out of the system. Insertion of the AlAs tunnel barriers is expected to enhance quantum-mechanica reflectivity of electrons in the AlO,BGa,,,As barrier at the heterointerface and improve the quality factor (Q-factor) of the QW resonator. This “highreflectance coating” of the QW resonator is expected to enhance the resonant effect. During MBE growth the sample was rotated in order to homogenize both the layer thickness and the composition ratio. However, the sample rotation was deliberately stopped when the GaAs well layer was grown, providing samples with varying well widths due to beam flux inhomogeneity. This alIowed us to systematically investigate the wellwidth dependence of the carrier capture efficiency by exploiting the PL mapping technique. PL measurements were carried out at various temperatures by using an Ar ion laser as an excitation source. A typical example of the PL spectrum at 77 K is shown in fig. 2. The luminescence is observed both from the QW and the Al,,,Ga,,,As barrier. The carrier capture efficiency was evaluated by the ratio of PL integrated intensity from the QW Cf,> and that from the barrier (I,). The PL mapping measurement gives us how the carrier capture efficiency depends on
r
I
7000
WAVELENGTH
I
1
8000
( A 1
Fig. 2. Photoluminescence spectra of Al,,,Ga,,As/CaAs quantum wells with AlAs tunnel barriers at 77 K with the excitation power of 1 mW.
77w I
7800 I,
.
0
7900 I
ema 1
I LTBr
-
206 77K
Fig. 3. Well-width dependence of 1,/I, in AI,,,Ga,,,As/ GaAs quantum wells with AlAs tunnel barriers at 77 K. Two resonant peaks are observed, which correspond to the resonance of the second and the third QW levels, respectively. Solid line represents the theoreqcal fit to the data with t,=195A.
the well width. Fig. 3 shows the well-width dependence (50-130 A) of &,,/I, at 77 K, for Otwo samples of L, = 50-90 A and L, = 90-130 A. It is clearly seen that the carrier capture efficiency strongly depends on the well width and exhibits tn oscillatory behavior. The first pea,k at L, = 67 A and the second peak at L, = 10’7A correspond to the resonances of the second and the third QW levels of electrons, respectively. We accounted for the results by the model based on a simple quantum-mechanical calculation. The model is analogous to the optical Fabry-Perot resonator, regarding the QW interface as a mirror of electron waves. In order to fit the results we took the loss of the electron wave coherency into account. The loss of electron wave coherency is thought to be due to the inelastic scattering in the well and/or the imperfection of interface mirrors. To simplify the calculation, we assumed that the square of the amplitude of the coherent electron wave exponentially decays in the well expressed as the parameter A(Z) = exp(-z/L,), where L, is the coherent length of the electron. That is, A(L,) represents the decay of the coherent eIectron when it crosses the well. To estimate the capture efficiency, the ratio of the square of the wavefunction of the electron in
A. Fujiwuru
644
et al. / Ohserr~ation of‘ rrsonunt electrorl captuw in AIGuAs / GuAs Q IV struc’trtw
the well (as averaged in the well) and that of the incident electron in the barrier was calculated by ICI, 1 = T
+%I
l-l
[A(&) i
+~(ul In4%) - 11V
sin(2k,l, + 2&A(
L,)
- 0) + sin H 2k,
L,
:
x([l-RA(fJ~-t4KA(L,) xsin’(k,L,-B)j-‘.
(1)
where R is the reflectivity of the interface mirror, T is the transmission coefficient through the interface mirror of incident electrons, 0 is the phase shift when the electron in the well is reflected back at the interface mirror, and k, is the wavenumber of the electron in the well. These parameters are dependent on the structure and are the functions of the incident electron energy. They can be calculated by the effective mass approximation [6] assuming the incident electron energy to be +kT and the band offset ratio of the conduction and the valence bands to be 65 :35 [7,8]. The solid line in fig. 3 shows the calculated result when the resoaant peak shape was fitted assuming L, = 195 A. A good agreement was obtained between the experiment and the calculation. As for the hole resonance, little effect was observed on the capture efficiency. The resonant electron capture was also observed even in the QW structure without AlAs tunnel barriers, though the effect was less propounced. The resonant peak appeared at L, = 86 A, corresponding to the resonance of the third QW level of the electron. The sharpness of the resonant peak, however, strongly depends on the temperature as seen in fig. 4. The solid lines arc the calculated results when L, is assumed to be 176, 88, and 48 A at 22, 33, and 44 K, respectively. The rapid degradation of the resonant peak means that the electron coherency loses with increasing temperature. Previously, we showed from PL excitation spectroscopy that the electron capture efficiency is rather reduced under the resonant condition [9]. That is, electrons captured in the well easily escape when the quantized level is close to the
Fig. 4. Well-width dependrnct: of I, /I,, in almplc ,\I,, i Ga,,,As/GaAs quantum wells at 32. 3.1, and 44 K. The peak corresponds the resonance of the third OW level of the electron. Solid lines represent the theoretical fits to the data 0 assuming I-, = 176. 88. and 48 A. respectively.
band-edge of the barrier. It should be born in mind, however. that the sample structure as well as the sample quality is quite different between these two experiments. The details will be reported separately. In summary, we report for the first time the observation of the resonant clcctron capture in AlGaAs/GaAs QW structures. It has been shown that the capture efficiency is drastically enhanced under the resonant electron condition. The calculation based on a simple model can fit the results well. Further details of the temperature dependcncc of the resonant effect will be rcportcd elsewhere. We are thankful to N. Ogasawara and Y. Katayama for fruitful discussion and S. Ohtakc for technical assistance.
References [II J.A. Burm and G. Bastard, Phys. Reb. B 3.1 (19X0) 1111). Microstrucr. 2 [?I M. Bahiker and B.K. Ridlely. Superlattice\ ( I’M) 1x7. [31 1-f. Shichijo. R.M. Kolhas. N. I lolonyah. Jr.. R.D. Dupu~\ and P.D. Dapkus, Solid State Common. 77 (107X)10X [41 B. Deveaud,
J. Shah. T.C. Damen and W.T. ‘Taang. ;Zppl. Phys. Lett. 52 (1986) 1X86. [51 D.Y. Oherli. J. Shah. J.L. Jewell, T.<‘. Damon and N. (‘hand, Appl. Phys. Lett. 54 (IW9) 1028.
A. Fujiwara et al. / Observation of resonant electron capture in AlGaAs / GaAs QWstructures [6] R, T, and 0 are expressed
as follows: 2
R=
%b(% - vb) cos ktbLth - i( v’,u~ - ci) %(%
T=
-i(
+ Ub) cos ktt&l
v,vb + vi)
sin ktbLtb
2
2C,Vlb Vlb(UW + Vh) cos ktbLtb -i( - I$ + L’,Cb
B= tan-’
tan L’,b(C,
+tan-’
-
-
2 “tb -
ub)
l.‘,Cb
kbkb
vwtib + ~1;) sin ktbLtb
1 1
tan ktbLtb c,b(cw
+ vb)
’
sin ktbLtb
,
’
645
where U, and vb are the group velocities of the electron in the well and in the barrier, respectively, while vtb and ktb are the imaginary group velocity and wavenumber of the electron in the tunnel barrier, respectively. [7] H. Kroemer, W.Y. Chien, J.S. Harris, Jr. and D.D. Edwall, Appl. Phys. Lett. 36 (1980) 295. [8] R.C. Miller, A.C. Gossard, D.A. Kleinman and 0. Munteanu, Phys. Rev. B 29 (1984) 3740. [9] N. Ogasawara, A. Fujiwara, N. Ohgushi, S. Fukatsu, Y. Shiraki, Y. Katayama and R. Ito, Phys. Rev. B 42 (1990) 9562.
Science
263 (1902) 642-645
surface science ::: ..:,.,’ ; : ,,,.. :“.
North-Holland
Observation of resonant well structures
WC dcmonstratc well\.
The sample
cat reflectivity quantized
for
of the electron.
time thin
efficiency
the lurrier
quantized
under
band-edge
tunnel
that the capture
dependent condition
capture
evidence
harriers
is ascribed
in AlGaAs/GaAs
tar the resonant
ckctl-on
on both 5idcs of the C;aAs well efficiency
on the well width
state in the well coincide\
the resonant
is found
the experrmenM
AlAs
It was found
state of the well is strongly
is such that the highest capture
the first
used contains
electron
with
of photogenerated
nnd increnw
under
the concluction-hnr,d
to the incread
capture
quantum
111AI<;~A\;C~:IA\
layer to cnhancc electrons
the resonant
in the r\lC;:tAs condition
edge ot the AIC;aA\
proluhility
that the clcctron
qu;~n~um
the qu~rntun~-rn~cli~~~~iwhere barr-icr.
harrier
into the
the well width The cnh;lnced
in the continuum
\t;ltt’
;~i
in the wcII
The capture of electrons and holes into ;I quantum well (QW) has ken attracting considerable intcrcst in terms of the device application and the underlying physical mechanism. The mechanism of carrier capture has been theoretically investigated from a quantum mechanical point of view 1121. Especially, the capture efficiency is expected to bc dependent on the well width and be enhanced under the resonant condition where the band-edge energy of the barrier is nearly equal to the highest QW level [I]. This resonant effect can bc understood by regarding a QW as a Fabry-Perot resonator of the incident electron wave in the barrier and are due to the interference of the coherent electron wave. Under the resonant condition, the wavefunction 01 incoming electrons from the barrier band-edge significantly accumulates in the well compared with the off-resonant condition. This is thought to lead to an increased capture efficiency. However. no experimental evidence of this effect has been presented so far [S-S]. In this paper, we report the first observation of the clcctron resonant capture in specially designed AlGaAs/GaAs QW
structures by means 01‘ photoluminescence (PL). It is demonstrated that the capture efficiency in a QW is dependent on the well width and is drastically enhanced under the resonant condition. The samples used wcrc grown by molecular beam cpitaxy (MBE) on semi-insulating GaAs (100) substrates. The band diagram of the htI-uclure is schematically illustrated in fig. I. .l‘he prominent feature is that thin AlAs tunnel harri-
GaAs oAI,Go,
7508
643
A. F~j~wa~a et al. / ~bser~~~t~~~ of remnant electron capture in AlGaAs / GaAs Q W st~~i~res
ers of 20 A are symmetrically inserted at heterointerfaces of the Al,,,Ga,.,As/GaAs QW structure and the QW structure is clad by AlAs layers to prevent carrier overflow out of the system. Insertion of the AlAs tunnel barriers is expected to enhance quantum-mechanica reflectivity of electrons in the AlO,BGa,,,As barrier at the heterointerface and improve the quality factor (Q-factor) of the QW resonator. This “highreflectance coating” of the QW resonator is expected to enhance the resonant effect. During MBE growth the sample was rotated in order to homogenize both the layer thickness and the composition ratio. However, the sample rotation was deliberately stopped when the GaAs well layer was grown, providing samples with varying well widths due to beam flux inhomogeneity. This alIowed us to systematically investigate the wellwidth dependence of the carrier capture efficiency by exploiting the PL mapping technique. PL measurements were carried out at various temperatures by using an Ar ion laser as an excitation source. A typical example of the PL spectrum at 77 K is shown in fig. 2. The luminescence is observed both from the QW and the Al,,,Ga,,,As barrier. The carrier capture efficiency was evaluated by the ratio of PL integrated intensity from the QW Cf,> and that from the barrier (I,). The PL mapping measurement gives us how the carrier capture efficiency depends on
r
I
7000
WAVELENGTH
I
1
8000
( A 1
Fig. 2. Photoluminescence spectra of Al,,,Ga,,As/CaAs quantum wells with AlAs tunnel barriers at 77 K with the excitation power of 1 mW.
77w I
7800 I,
.
0
7900 I
ema 1
I LTBr
-
206 77K
Fig. 3. Well-width dependence of 1,/I, in AI,,,Ga,,,As/ GaAs quantum wells with AlAs tunnel barriers at 77 K. Two resonant peaks are observed, which correspond to the resonance of the second and the third QW levels, respectively. Solid line represents the theoreqcal fit to the data with t,=195A.
the well width. Fig. 3 shows the well-width dependence (50-130 A) of &,,/I, at 77 K, for Otwo samples of L, = 50-90 A and L, = 90-130 A. It is clearly seen that the carrier capture efficiency strongly depends on the well width and exhibits tn oscillatory behavior. The first pea,k at L, = 67 A and the second peak at L, = 10’7A correspond to the resonances of the second and the third QW levels of electrons, respectively. We accounted for the results by the model based on a simple quantum-mechanical calculation. The model is analogous to the optical Fabry-Perot resonator, regarding the QW interface as a mirror of electron waves. In order to fit the results we took the loss of the electron wave coherency into account. The loss of electron wave coherency is thought to be due to the inelastic scattering in the well and/or the imperfection of interface mirrors. To simplify the calculation, we assumed that the square of the amplitude of the coherent electron wave exponentially decays in the well expressed as the parameter A(Z) = exp(-z/L,), where L, is the coherent length of the electron. That is, A(L,) represents the decay of the coherent eIectron when it crosses the well. To estimate the capture efficiency, the ratio of the square of the wavefunction of the electron in
A. Fujiwuru
644
et al. / Ohserr~ation of‘ rrsonunt electrorl captuw in AIGuAs / GuAs Q IV struc’trtw
the well (as averaged in the well) and that of the incident electron in the barrier was calculated by ICI, 1 = T
+%I
l-l
[A(&) i
+~(ul In4%) - 11V
sin(2k,l, + 2&A(
L,)
- 0) + sin H 2k,
L,
:
x([l-RA(fJ~-t4KA(L,) xsin’(k,L,-B)j-‘.
(1)
where R is the reflectivity of the interface mirror, T is the transmission coefficient through the interface mirror of incident electrons, 0 is the phase shift when the electron in the well is reflected back at the interface mirror, and k, is the wavenumber of the electron in the well. These parameters are dependent on the structure and are the functions of the incident electron energy. They can be calculated by the effective mass approximation [6] assuming the incident electron energy to be +kT and the band offset ratio of the conduction and the valence bands to be 65 :35 [7,8]. The solid line in fig. 3 shows the calculated result when the resoaant peak shape was fitted assuming L, = 195 A. A good agreement was obtained between the experiment and the calculation. As for the hole resonance, little effect was observed on the capture efficiency. The resonant electron capture was also observed even in the QW structure without AlAs tunnel barriers, though the effect was less propounced. The resonant peak appeared at L, = 86 A, corresponding to the resonance of the third QW level of the electron. The sharpness of the resonant peak, however, strongly depends on the temperature as seen in fig. 4. The solid lines arc the calculated results when L, is assumed to be 176, 88, and 48 A at 22, 33, and 44 K, respectively. The rapid degradation of the resonant peak means that the electron coherency loses with increasing temperature. Previously, we showed from PL excitation spectroscopy that the electron capture efficiency is rather reduced under the resonant condition [9]. That is, electrons captured in the well easily escape when the quantized level is close to the
Fig. 4. Well-width dependrnct: of I, /I,, in almplc ,\I,, i Ga,,,As/GaAs quantum wells at 32. 3.1, and 44 K. The peak corresponds the resonance of the third OW level of the electron. Solid lines represent the theoretical fits to the data 0 assuming I-, = 176. 88. and 48 A. respectively.
band-edge of the barrier. It should be born in mind, however. that the sample structure as well as the sample quality is quite different between these two experiments. The details will be reported separately. In summary, we report for the first time the observation of the resonant clcctron capture in AlGaAs/GaAs QW structures. It has been shown that the capture efficiency is drastically enhanced under the resonant electron condition. The calculation based on a simple model can fit the results well. Further details of the temperature dependcncc of the resonant effect will be rcportcd elsewhere. We are thankful to N. Ogasawara and Y. Katayama for fruitful discussion and S. Ohtakc for technical assistance.
References [II J.A. Burm and G. Bastard, Phys. Reb. B 3.1 (19X0) 1111). Microstrucr. 2 [?I M. Bahiker and B.K. Ridlely. Superlattice\ ( I’M) 1x7. [31 1-f. Shichijo. R.M. Kolhas. N. I lolonyah. Jr.. R.D. Dupu~\ and P.D. Dapkus, Solid State Common. 77 (107X)10X [41 B. Deveaud,
J. Shah. T.C. Damen and W.T. ‘Taang. ;Zppl. Phys. Lett. 52 (1986) 1X86. [51 D.Y. Oherli. J. Shah. J.L. Jewell, T.<‘. Damon and N. (‘hand, Appl. Phys. Lett. 54 (IW9) 1028.
A. Fujiwara et al. / Observation of resonant electron capture in AlGaAs / GaAs QWstructures [6] R, T, and 0 are expressed
as follows: 2
R=
%b(% - vb) cos ktbLth - i( v’,u~ - ci) %(%
T=
-i(
+ Ub) cos ktt&l
v,vb + vi)
sin ktbLtb
2
2C,Vlb Vlb(UW + Vh) cos ktbLtb -i( - I$ + L’,Cb
B= tan-’
tan L’,b(C,
+tan-’
-
-
2 “tb -
ub)
l.‘,Cb
kbkb
vwtib + ~1;) sin ktbLtb
1 1
tan ktbLtb c,b(cw
+ vb)
’
sin ktbLtb
,
’
645
where U, and vb are the group velocities of the electron in the well and in the barrier, respectively, while vtb and ktb are the imaginary group velocity and wavenumber of the electron in the tunnel barrier, respectively. [7] H. Kroemer, W.Y. Chien, J.S. Harris, Jr. and D.D. Edwall, Appl. Phys. Lett. 36 (1980) 295. [8] R.C. Miller, A.C. Gossard, D.A. Kleinman and 0. Munteanu, Phys. Rev. B 29 (1984) 3740. [9] N. Ogasawara, A. Fujiwara, N. Ohgushi, S. Fukatsu, Y. Shiraki, Y. Katayama and R. Ito, Phys. Rev. B 42 (1990) 9562.