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RAMAN STUDY OF THE ANHARMONICITY AND
DISORDER-INDUCED EFFECTS IN Ga1-xAlxAs
Bernard Jusserand, J. Sapriel, F. Alexandre, P. Delpech
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C6, supple'ment au nO1 2, Tome 42, de'cembre 1981 page C6-43
RAMAN
STUDY OF THE ANHARMONICITY AND DISORDER-INDUCED EFFECTSIN
Gal-xA1xAs
B. Jusserand, J. Sapriel, F. Alexandre and P. Delpech
Centre NationaZ drEtudes des Te'Ze'comnications, 196 rue de Paris, 92220 Bagneux, France
ABSTRACT.- Raman measurements of the frequency shift and profile variations versus temperature are interpreted in ternsof anharmo- nicity and disorder. Several disorder activated longitudinal and transverse acoustic modes have been observed and assigned. A des- cription of their resonant behaviour is also given.
1.Study of the first-order Raman lines.-
The emergency of a low-energy tail in the LO-lines has been alrea- dy reported in ~ a A 1 ~ s ) In order to analyze the origin of this asymme- try we have investigated the frequency and profile of the LO peak in GaAs and Ga0-73A10,27A~ as a function of the temperature T.
The effective half-width
r
and the anharmonic shift A of a Raman peak of frequency w are respectively given by Re1 (1) and (2)r = r
+ r1 3 ( 1 )
A = BT
+
A3+
A4 ( 2 )r3
is due to cubic anharmonicity andrl
is a damping independent of T due to other attenuation processes. Ouartic anharmonicity is neglected in (1) as it qives rise to higher order contribution to the linewidth; A3 and A 4 are the shifts due to cubic and quartic anharmonicity respec- tively and BT is the contribution of the thermal expansion. The cubic process consists of the decay of the optical phonon into two acoustic phonons of frequency w / 2 and of equal and opposite wave vector. For a- coustic phonons whose wave vector is far from the Brillouin zone edge, where frequency-independent density of states can be reasonably assumed, one finds$'
r3
=rS)
[2n(w/2)+1] (3) A~ =-
r3
A(q) ( 4 )n is the thermal population factor n(w) = [exp(hw/kT) -11 q is the reduced wave vector of the acoustic phonons involved in the process and ~ ( q ) = [1/(4q4) + 1/(3q3)
+
1/(2q2) + l/q + In (l/q-111
/ T (5)Relations (3)-(5) are valid in the case of the LO and TO modes in GaAs and in the case of the GaAs-type modes in Gal-xA1 As where
X
q = 0.5. The constant B of equ.(2) is calculated from data of the lite- rature relative to elastic constants, thermal expansion and Ranbanshifts
C6-44 JOURNAL DE PHYSIQUE
under hydrostatic pressure in GaAs. One finds l? = - 0 . 5 8 ~ 1 0 - ~ c m - ~ ~ - ~ . Raman scattering experiments of the LO and TO modes in GaAs and of the LO GaAs-type in GaO. 73A10. 2 7 A ~ have been performed3between 20 and 450K. The peak frequency and the profile have been carefully investigated. Fitting re1 (1) -(5) to our experimental results, we found A4 negligible with respect to A 3 and obtained the values of I'l,I'y and Q ( Q = @-A is the frequency of the phonon in the perfectly harmonic lattice) which are reported in Table 1.
TO in 0 0.24 273 GaAs LC in 0.28 0.26 297 GaAs 1-11 0.28 287 mode for x = 0.27
Table 1- Parameters determined by fifting our experimental re- sults to relations (1)
-
(5) ;the anharmonic contribution to the residual low temperature damping is expressed. by
r0
3'
One can see that
r:
has the same value in GaAs and GaAlAs. The anharmonicity is not affected by the disorder. The asymmetry of the LO mode in GaAlAs is not a consequence of the anharmonicity. Complementa- ry experiments on several samples for x in the range 0-0.5 have che- cked that the asymmetry was temperature independent. It is interpreted as a disorder induced effect, the low-energy tail being due to contri- bution of LO phonons in the vicinity of k=O, whose enerqy is smaller.3 A phenomenological model of this effect is given elsewhere
.
2. Study of the disorder-activated acoustic modes. As one approaches the middle-range concentration in Gal-xAlxAs, new modes appear in the low-frequency part of the Raman spectra which are very weak and clear- ly resolved only under resonance conditions. Such conditions were rea- lized in a Ga0.25A10.75A~ sample since the extrema at k = 0 of the conduction and valence band are, for this composition, separated by an amount of energy which lies in the range of the argon-ion laser emit-
0
ton and the value of the gap at k=O. The increase of these intensities is only a consequence of the tuning of this gap to the incident light when the temperature is made to vary. Peaks I-V are therefore first order Raman lines which reflects the density of states
.
A linear in- terpolation between the values of wTA(L) and. wTA (XI in GaAs and AlAs gives : w
TA (L) = 75 cm-I and w TA(X) = 97 cm- for x = 0.75. These values are very close to the frequencies of peaks I and 11, who- se assignment is straightforward. Peaks IV and V situated at 200 cm-1 and 210 cm-I can be assigned as the LA(L) and LA(X) modes. Peak IV is the same as the peak reported in Ref.4
.
Peak V is an additional one which undergoes a resonance clearly stronger than all others. We report in Fig.2 the intensity variations of the Raman lines at 80 K for five+
Ar laser lines. The resonance behaviour of line I,II,EEland IV is qui- te similar to that observed for the GaAs-t-ype and AlAs-type LO modes in the allowed configurationsthoughline V has a "forbidden resonant behaviour". The polarized Raman study shows a I'l symmetry for the DALA structure as predicted theoretically. The DATA structure is preferen- tially
rl
polarized although the theory predand I' 15' D A ~ A ...
4880j
, D ~ T A , '"'
----5145A ...---______
I I I I 200 150 100 50FREQUENCY-SHIFT(C~-~) INCIDENT WAVELENGTH
(A)
Fig.1 : Disorder-activated longitudi- Fig.2 : Incident wavelength nal-acoustic structure (DALA) and dependence of the intensity. Disorder-activated transverse-acous- xA1As-type LO (FC)
.
tic structure (DATA) in GaO. 2!A10. 75AS +AlAs-type LO (AC)
.
Peaks I,II,IV and V are asslgned as OGaAs-type LO (FC).
TA (L),
TA(X),
LA(L) and LA(X) respec- mGaAs-type LO (AC).
tively. oPeak V (xlO)
APeak i,II,m (x10) and I11 (~50) FC : Forbidden configura-
tion.
AC : Allowed configuration.
References : 1. J. Shah, A.E. Di Giovani, T.C. Damen, and B.I. Miller, Phys. Rev. B, 7, 3481 (1973).
2. A.S. Pine and F . E . Tannenwald, Phys. Rev. B,
