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Characterization of GaAsAlAs superlattices by laser-Raman spectroscopy
Solid State Communications, Vol. 49, No. 2, pp. 157-159, 1984. Printed in Great Britain.
0038-1098]84 $3.00 + .00 Pergamon Press Ltd.
CHARACTERIZATION OF GaAs-AlAs SUPERLATTICES BY LASER-RAMAN SPECTROSCOPY K. Kubota, M. Nakayama, H. Katoh and N. Sano Faculty of Science, Kwansei Gukuin University, Nishinomiya -662, Japan
(Received 3 September 1983 by J. Kanamori) Measurements of Raman scattering were performed on GaAs-AIAs superlattices. The lattice period ranged from 12 to 3000 A. Phonon frequencies were shifted by changing the layer thickness. Qualitative expression of this shift and crystalline perfection are discussed. RAMAN SCATTERING in multiple GaAs-A1As heterostructure has recently received much attention. In this letter we report the Raman investigation of GaAs-AlAs superlattices over a wide range of individual layer thickness. We characterize the crystalline quality and interdiffusion between GaAs and ALAs. The samples were layers of the total thickness of several micrometers which were grown by molecular beam epitaxy on a GaAs substrate oriented such that the layers were perpendicular to the (0 0 1) direction. Layer thickness of GaAs and AlAs were 5 )k ~ 1800/k, and layers ranging from lattice periodicities of 12 to 3000 )k were measured. In a present experiment the layer thickness of GaAs was taken to be 1.5 times as large as that of AlAs for each sample. These layer thicknesses and the lattice periodicities were confirmed by the X-ray diffraction measurement. All the Raman measurements were made at room temperature on (0 0 1) faces in backscattering geometry with a 5145-)k line of an Ar ÷ laser. In this geometry, scattering from the transverse optic (TO) mode is forbidden. Obtained spectra were compared with the data of pure GaAs, AlAs and GaI_xAlxAs alloys. Figure 1 shows Raman spectra of superlattices with periods of 7A GaAs-5 A AlAs and 100h GaAs-70 A ALAs. The feature is the definite shift in energy of the principal GaAs-like (~ 290 cm -1) and AlAs-like (~ 400 cm -1) longitudinal optic (LO) phonons in changing periods. Furthermore, the spectra show broader features on the low-energy side of the LO modes which have another peak at the frequencies corresponding to the TO mode of pure GaAs and ALAs. The dependence of peak phonon frequencies on the one-layer thickness is given in Fig. 2. Frequencies of pure GaAs, AlAs and a Gao.6 AIo.4As alloy are also indicated on the right-hand and left-hand sides in the figure, respectively [1 ]. When the one-layer thickness is above 50 A, the Raman shifts are almost the same as the pure one, while below this thickness they decrease to those of GaA1As alloys. The sharpness of LO phonon lines means a high
degree of crystal perfection in the superlattice structure of GaAs and AlAs: the sharp rise on the higher-energy side of the LO modes indicates the lack of the GaAlAs alloy component in the GaAs-AlAs inteface regions. The very-slow growth-rate of the sample (~ A sec -1) and the monotonic decrease of the observed frequencies with decreasing the layer thickness below 50 A suggest also the lack of the layer-period fluctuation in multiple heterostructures. However, it is possible that the interface between GaAs and AlAS takes irregular distribution of island-like structures by mono GaAs- or AlAs-layer thickness (~ 2.83 A). This increases the complexity of the interface, and would give rise to TO phonon modes for the thinner layer-thickness samples. The anisotropy induced by the layering effect or the strain induced on the heterostructure may generate the shift of phonon frequencies toward the lower-energy side by decreasing the layer period. On the other hand, Barker et al. [2] disucssed the problem according to the linear chain model of cations (Ga and AI) and anions (As) as for a superlattice, assuming the complete separation of longitudinal and transverse vibrations for phonons with the wave vector perpendicular to the face of the superlattice. As a result, the Raman shift of the superlattice with the sequence of monolayers is shown lower than those of the bilayer structure. We take also as a superlattice model a linear chain of G a - A s - A l - A s . Only vibrations along the chain are considered (LO modes). The vibrational force constant between As and A1 is/3~, and that between As and Ga is ~2- Nearest neighbors are considered, and Coulomb effects are ignored. We calculate a vibrational frequency oa at the zero wave vector for Raman scattering. By using the fact that the atomic mass of A1 (m 1) is much smaller than that of Ga (m2) and of As (M) and ~1 is not much different from/~2, the approximate calculation gives two characteristic frequencies; [ 1 +/3,+~32__ m ] w~ ~ 2 13, m--7 2 2 '
157
(1)
158
CHARACTERIZATION OF GaAs-AIAs SUPERLATTICES AtAso-type ( L0 )
400 ~lalAl,4As ttl
~00~,- 70A
¢.-
• LOI o T
.
o
AIA~,q
o o o (TO)
E
u
a5
Vol. 49, No. 2
TO"
,TO+ 350
LL >.
~
F--
300
uo z ILl FZ
• •
GaAS- type ( kO ) •
t_'°2 £1£
•
~
•
t,
GOAS LO-
<.,.o, •
•
•
TO'+
•
/
,
t
1o 100 S S,0~O~ ) ONE-LAYER THICKNE
Z
,5----
Fig. 2. Observed frequencies of principal phonons of superlattices. The abscissa is of the one-layer thickness.
~E Oc
16 I
i
1
e
3OO
200 RAMAN
I
AlAs-type
t
0~0 ~ 0
40O
SHIFT (cm-')
Fig. 1. Raman spectra of 7A GaAs-5 A AlAs and 100 A GaAs-70 .& AlAs superlattices.
~ o / 0 0
jo
,_. 15 T E g
/.-o
o 14 oa=2 -"" -2 bS=M~-7 +] ~' - - 2+/3a
,
(2)
where the former is called the AlAs-type mode and the other the GaAs-type mode, When we compare with the expression of the usual two-atom linear chain (pure GaAs or AlAs), the mass of an As atom in the above equations is twice as large as that in the two-atom case, assuming #1 -~/32. Namely, the frequency of the monolayer superlattice is lower than that of pure GaAs or ALAs. Similar calculations of the linear-chain model are possible for superlattiees with thicker layers. However, for the simple qualitative discussion, we assume a reduced monolayer model by introducing the average value of a probability which discribes that the neighboring atom next to an As atom is a different kind from that of the opposite-side atom. For the superlattice layer where n Ga atoms are arranged between As atoms, followed by a series of AI-As pairs, the average probability a for the GaAs layer is =
1 n
-.
(3)
Pure GaAs or AlAs takes a = O, and a monolayer superlattice corresponds to a = 1. Using this probability, we modify the frequencies for the rough estimations; [ 1 +(2--a).~,+a152 1 ] oa~ = 2 ~t m'-7 2 (1 + a ) M '
(4)
9
"a
t,.~ +.~+~
GaAs-tyloe
/ /Q
I
I
0.5
0.6
I
o.7
I
0.8
I
I
0.9
Lo
I/(1-~')
Fig. 3. Experimental data in Fig. 2 are arranged according to equations (4) and (5). w~ = 2[/32m~4OtCJ,+(2--oO~ ~ 1 ] 2 (1 + a ) M "
(5)
For example, the one-layer thickness of 50 A corresponds to n = 50 •/2.83 A ~-- 18 and a ~ 0.06, and the frequencies are nearly equal to the usual two-atom case (pure GaAs and AlAs). Equations (4) and (5) are linear functions of (1 + ~)-1. Agreement with the experimental data is very well, as shown in Fig. 3. In conclusion, the shift of the phonon frequencies with the layer thickness was qualitatively described: the GaAs-A1As superlattices made by molecular beam epitaxy have high crystalline quality and fairly good interfaces down to the lattice period of ~ 20 A. These
Vok 49, No. 2
CHARACTERIZATION OF GaAs-A1As SUPERLATTICES
conclusions support the experimental results of photoluminescence measurements [3].
Acknowledgements - The MBE facilities were supported by the Yamada Science Foundation. The authors would like to acknowledge the assistance of Mr S. Matsudaira in making measurements.
159
REFERENCES 1.
2. 3.
R. Tsu, H. Kawamura & L. Esaki, in Proceedings of the International Conference on the Physics of Semiconductors, Warsaw, 1972 Vol. 2, p. 1135. Elsevier, Amsterdam, (1972). A.S. Barker Jr., J.L. Mertz & A.C. Gossard, Phys. Rev. B17, 3181(1978). Y. Horikoshi & H. Okamoto, Physics Monthly (in Japanese) 4,302 (1983).
0038-1098]84 $3.00 + .00 Pergamon Press Ltd.
CHARACTERIZATION OF GaAs-AlAs SUPERLATTICES BY LASER-RAMAN SPECTROSCOPY K. Kubota, M. Nakayama, H. Katoh and N. Sano Faculty of Science, Kwansei Gukuin University, Nishinomiya -662, Japan
(Received 3 September 1983 by J. Kanamori) Measurements of Raman scattering were performed on GaAs-AIAs superlattices. The lattice period ranged from 12 to 3000 A. Phonon frequencies were shifted by changing the layer thickness. Qualitative expression of this shift and crystalline perfection are discussed. RAMAN SCATTERING in multiple GaAs-A1As heterostructure has recently received much attention. In this letter we report the Raman investigation of GaAs-AlAs superlattices over a wide range of individual layer thickness. We characterize the crystalline quality and interdiffusion between GaAs and ALAs. The samples were layers of the total thickness of several micrometers which were grown by molecular beam epitaxy on a GaAs substrate oriented such that the layers were perpendicular to the (0 0 1) direction. Layer thickness of GaAs and AlAs were 5 )k ~ 1800/k, and layers ranging from lattice periodicities of 12 to 3000 )k were measured. In a present experiment the layer thickness of GaAs was taken to be 1.5 times as large as that of AlAs for each sample. These layer thicknesses and the lattice periodicities were confirmed by the X-ray diffraction measurement. All the Raman measurements were made at room temperature on (0 0 1) faces in backscattering geometry with a 5145-)k line of an Ar ÷ laser. In this geometry, scattering from the transverse optic (TO) mode is forbidden. Obtained spectra were compared with the data of pure GaAs, AlAs and GaI_xAlxAs alloys. Figure 1 shows Raman spectra of superlattices with periods of 7A GaAs-5 A AlAs and 100h GaAs-70 A ALAs. The feature is the definite shift in energy of the principal GaAs-like (~ 290 cm -1) and AlAs-like (~ 400 cm -1) longitudinal optic (LO) phonons in changing periods. Furthermore, the spectra show broader features on the low-energy side of the LO modes which have another peak at the frequencies corresponding to the TO mode of pure GaAs and ALAs. The dependence of peak phonon frequencies on the one-layer thickness is given in Fig. 2. Frequencies of pure GaAs, AlAs and a Gao.6 AIo.4As alloy are also indicated on the right-hand and left-hand sides in the figure, respectively [1 ]. When the one-layer thickness is above 50 A, the Raman shifts are almost the same as the pure one, while below this thickness they decrease to those of GaA1As alloys. The sharpness of LO phonon lines means a high
degree of crystal perfection in the superlattice structure of GaAs and AlAs: the sharp rise on the higher-energy side of the LO modes indicates the lack of the GaAlAs alloy component in the GaAs-AlAs inteface regions. The very-slow growth-rate of the sample (~ A sec -1) and the monotonic decrease of the observed frequencies with decreasing the layer thickness below 50 A suggest also the lack of the layer-period fluctuation in multiple heterostructures. However, it is possible that the interface between GaAs and AlAS takes irregular distribution of island-like structures by mono GaAs- or AlAs-layer thickness (~ 2.83 A). This increases the complexity of the interface, and would give rise to TO phonon modes for the thinner layer-thickness samples. The anisotropy induced by the layering effect or the strain induced on the heterostructure may generate the shift of phonon frequencies toward the lower-energy side by decreasing the layer period. On the other hand, Barker et al. [2] disucssed the problem according to the linear chain model of cations (Ga and AI) and anions (As) as for a superlattice, assuming the complete separation of longitudinal and transverse vibrations for phonons with the wave vector perpendicular to the face of the superlattice. As a result, the Raman shift of the superlattice with the sequence of monolayers is shown lower than those of the bilayer structure. We take also as a superlattice model a linear chain of G a - A s - A l - A s . Only vibrations along the chain are considered (LO modes). The vibrational force constant between As and A1 is/3~, and that between As and Ga is ~2- Nearest neighbors are considered, and Coulomb effects are ignored. We calculate a vibrational frequency oa at the zero wave vector for Raman scattering. By using the fact that the atomic mass of A1 (m 1) is much smaller than that of Ga (m2) and of As (M) and ~1 is not much different from/~2, the approximate calculation gives two characteristic frequencies; [ 1 +/3,+~32__ m ] w~ ~ 2 13, m--7 2 2 '
157
(1)
158
CHARACTERIZATION OF GaAs-AIAs SUPERLATTICES AtAso-type ( L0 )
400 ~lalAl,4As ttl
~00~,- 70A
¢.-
• LOI o T
.
o
AIA~,q
o o o (TO)
E
u
a5
Vol. 49, No. 2
TO"
,TO+ 350
LL >.
~
F--
300
uo z ILl FZ
• •
GaAS- type ( kO ) •
t_'°2 £1£
•
~
•
t,
GOAS LO-
<.,.o, •
•
•
TO'+
•
/
,
t
1o 100 S S,0~O~ ) ONE-LAYER THICKNE
Z
,5----
Fig. 2. Observed frequencies of principal phonons of superlattices. The abscissa is of the one-layer thickness.
~E Oc
16 I
i
1
e
3OO
200 RAMAN
I
AlAs-type
t
0~0 ~ 0
40O
SHIFT (cm-')
Fig. 1. Raman spectra of 7A GaAs-5 A AlAs and 100 A GaAs-70 .& AlAs superlattices.
~ o / 0 0
jo
,_. 15 T E g
/.-o
o 14 oa=2 -"" -2 bS=M~-7 +] ~' - - 2+/3a
,
(2)
where the former is called the AlAs-type mode and the other the GaAs-type mode, When we compare with the expression of the usual two-atom linear chain (pure GaAs or AlAs), the mass of an As atom in the above equations is twice as large as that in the two-atom case, assuming #1 -~/32. Namely, the frequency of the monolayer superlattice is lower than that of pure GaAs or ALAs. Similar calculations of the linear-chain model are possible for superlattiees with thicker layers. However, for the simple qualitative discussion, we assume a reduced monolayer model by introducing the average value of a probability which discribes that the neighboring atom next to an As atom is a different kind from that of the opposite-side atom. For the superlattice layer where n Ga atoms are arranged between As atoms, followed by a series of AI-As pairs, the average probability a for the GaAs layer is =
1 n
-.
(3)
Pure GaAs or AlAs takes a = O, and a monolayer superlattice corresponds to a = 1. Using this probability, we modify the frequencies for the rough estimations; [ 1 +(2--a).~,+a152 1 ] oa~ = 2 ~t m'-7 2 (1 + a ) M '
(4)
9
"a
t,.~ +.~+~
GaAs-tyloe
/ /Q
I
I
0.5
0.6
I
o.7
I
0.8
I
I
0.9
Lo
I/(1-~')
Fig. 3. Experimental data in Fig. 2 are arranged according to equations (4) and (5). w~ = 2[/32m~4OtCJ,+(2--oO~ ~ 1 ] 2 (1 + a ) M "
(5)
For example, the one-layer thickness of 50 A corresponds to n = 50 •/2.83 A ~-- 18 and a ~ 0.06, and the frequencies are nearly equal to the usual two-atom case (pure GaAs and AlAs). Equations (4) and (5) are linear functions of (1 + ~)-1. Agreement with the experimental data is very well, as shown in Fig. 3. In conclusion, the shift of the phonon frequencies with the layer thickness was qualitatively described: the GaAs-A1As superlattices made by molecular beam epitaxy have high crystalline quality and fairly good interfaces down to the lattice period of ~ 20 A. These
Vok 49, No. 2
CHARACTERIZATION OF GaAs-A1As SUPERLATTICES
conclusions support the experimental results of photoluminescence measurements [3].
Acknowledgements - The MBE facilities were supported by the Yamada Science Foundation. The authors would like to acknowledge the assistance of Mr S. Matsudaira in making measurements.
159
REFERENCES 1.
2. 3.
R. Tsu, H. Kawamura & L. Esaki, in Proceedings of the International Conference on the Physics of Semiconductors, Warsaw, 1972 Vol. 2, p. 1135. Elsevier, Amsterdam, (1972). A.S. Barker Jr., J.L. Mertz & A.C. Gossard, Phys. Rev. B17, 3181(1978). Y. Horikoshi & H. Okamoto, Physics Monthly (in Japanese) 4,302 (1983).