RAMAN PROBING OF PHONONS AND INTERFACES IN SEMICONDUCTOR SUPERLATTICES

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RAMAN PROBING OF PHONONS AND INTERFACES IN SEMICONDUCTOR

SUPERLATTICES

M. Klein, C. Colvard, R. Fischer, H . Morkoç

To cite this version:

M. Klein, C. Colvard, R. Fischer, H . Morkoç. RAMAN PROBING OF PHONONS AND INTER- FACES IN SEMICONDUCTOR SUPERLATTICES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-131-C5-137. �10.1051/jphyscol:1984519�. �jpa-00224137�

JOURNAL DE PHYSIQUE

Colloque C5, supplbment au n04, Tome 45, avril 1984 page C5-131

RAMAN PROBING OF PHONONS AND INTERFACES IN SEMICONDUCTOR SUPERLATTICES

M.V. ~ l e i n l , ~ ~ 3 , C. ~olvardl,~, R. ~ i s c h e r ~ ~ ~ and H. ~ o r k o ~ ~ r ~ Department of Physics1, Materials Research Laboratory2, Coordinated Science Laboratory3 and Department of E l e c t r i c a l ~ n g i n e e r i n g ~ , University of I l l i n o i s a t Urbana-Champaign, Urbana, IL 61801, U . S.A

.

RQsum6 - Dans cet article, nous prlsentons des mesures de diffusion Raman dans un grand nombre de superr'eseaux.

Les frgquences observges sont en accord avec un modgle glastique dgcrivant un matgriel construit avec des couches alternges. Un modile continu decrivant les intensit'es observges par diffusion Raman s'applique bien dans des conditions non-rssonnantes.

Abstract

-

Many properties of semiconductor superlattices (SL) and multiple quantum well

(MQW) heterostructures have now been studied. Interest has grown in parallel

with the ability to grow good quality samples with sharp interfaces. Much effort has lead to good understanding of the two-dimensional effects caused by confine- ment of electrons in the quantum wells. Only when the barriers are thin does three-dimensional electron behavior begin. Much less experimental work has been reported on phonons in superlattices. The most dramatic effects result from zone folding, and this paper will concentrate on them.

Raman studies of folded acoustic phonons have now been reported by several groups 11-41. Unlike the case of electronic energy levels, which show confine- ment, these phonon modes show coherence across many layers. They therefore provide information about layer-to-layer uniformity that complements that from probes of confined electron states. The SL periodicity shrinks the bulk Brillouin zone into a mini-zone, folds the phonon dispersion curves, and opens small gaps due to Bragg reflection. We have used Raman scattering to study these folded phonons in a number of SL samples grown by molecular beam epitaxy (MBE) and present here some of the results.

The samples have periods between 25 and 200 A and consist of alternate layers of GaAs and AlxGal-xAs with various x values grown on [001] oriented GaAs sub- strates. Most of the Raman data presented here were taken at room temperature in a Brewster angle, backscattering geometry. For incident light polarized along

[loo] and scattered light polarized along [OIO], denoted (x,y), the Raman

selection rules allow only modes of B2 symmetry to be observed if the crystal has D2d symmetry. For the (x,x) geometry only A1 modes are allowed.

The [001] dispersion for an LA phonon shown in the inset of Fig. 1 demon- strates the effect of the layering on longitudinal modes in a SL with 42 a ^GaAs

and 8 A10 3Ga 7As per period. Gaps appear at the zone center and edge, whereas at low ?;equencies the remaining dispersion is essentLally linear. This

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984519

C5-132 JOURNAL DE PHYSIQUE

curve was calculated using an elastic continuum model for acoustic phonons, i.e.

a Kronig-Penney model for phonons. /5,2,4/ The crosses represent the lowest three orders of folded phonons that can conserve momentum while scattering light of 5145 A wavelength. The phonon wave-vector is nearly normal to the layers and is given by

where n is the refractive index at wavelength hL. We assume n to be the same as that in an alloy with the same average A1 content. The calculations show that for frequencies away from the small gaps the folded phonons occur as doublets with frequencies

where m is an integer and

and where

Such results are obtained by neglecting the perturbation caused by the SL on zero-order plane waves propagating with velocity GSL.

I I

Figure 1 - Raman spectrum at hL = 5145 A of a SL with 100 periods of 42 a GaAs- 8 a A1 3Ga ,As showing folding up to A = 1 and a 2 TA struc- ture. Insert indicates qZ of folded doublets.

0

J

0 40 80 120 160 200

WAVENUMBER SHIFT

The Raman spectrum in Fig. 1 shows data taken from such a SL using 5145 a

laser light. Apparent are the doublets corresponding to m = 1 to 3 and a 2TA structure whose origin may be partly due to the GaAs substrate. The A1 component appears in the upper (x,x) curve. The absence of any B2 scattering in the lower (x,y) curve is due to the effective inversion symmetry of the SL seen by these long-wavelength acoustic modes. /4/ The B2 part of the spectrum would represent the odd-parity component of the vibrations, and coupling to it would be forbidden for Raman scattering in a lattice with inversion symmetry. The peak at 15 cm-I is related to the zone boundary. Its appearance seems to be a general phenome- non, but it will not be further discussed here.

Figure 2 shows spectra from a sample with 13.9 A GaAs and _{1 l . b} A AlAs per period. One again sees the m = 1 longitudinal doublet near 67 cm-' and in addition small peaks near 45 cm-' due to transverse phonons. These latter modes have E-symmetry in the SL, and this is a forbidden geometry for backscattering from a [001] face. However the Brewster angle geometry used here introduces a small z-component of polarization, which may account for their appearance.

Disorder may also play a role.

10

\ r, C

F i g u r e 2 - Raman s p e c t r u m ij 0

; E - of a 13.9

a

SL w i t h X L = 5145 8 . E-sym- m e t r y t r a n s v e r s e phonons a r e

'

l g

," tx. X )

The sample u s e d f o r F i g . 2 was a l s o u s e d t o d e t e r m i n e t h e phonon d i s p e r s i o n t o t h e e x t e n t t h a t t h e phonon wavevector q, c a n be v a r i e d by v a r y i n g X L between 4579 8 and 6764 8 . The r e s u l t s a r e shown i n F i g . 3 , and a r e compared w i t h c a l c u - l a t i o n s u s i n g a l i n e a r c h a i n model w i t h 5 monolayers of GaAs and 4 monolayers of AlAs p e r p e r i o d . Atomic masses were u s e d , and t h e s i n g l e f o r c e c o n s t a n t was c h o s e n t o p r o v i d e t h e c o r r e c t sound v e l o c i t y f o r b u l k GaAs. For l a r g e r p e r i o d s t h i s t y p e of model a g r e e s w i t h t h e e l a s t i c continuum model mentioned above. / 6 / Note t h a t even w i t h s u c h a s m a l l p e r i o d we a r e j u s t b a r e l y i n t h e r e g i o n where Bragg r e f l e c t i o n c a u s e s c u r v a t u r e i n t h e d i s p e r s i o n c u r v e s , i . e , , p a r t i a l l y changes t h e z e r o - o r d e r r u n n i n g wave i n t o a s t a n d i n g wave.

The r e s u l t s of measurements on a v a r i e t y of samples a r e summarized i n Fig. 4 , where t h e f r e q u e n c y of t h e f o l d e d phonon d o u b l e t s i s p l o t t e d v e r s u s d-l. The a v e r a g e sound v e l o c i t y cSL v a r i e s w i t h A1 c o n t e n t , b u t t h e t r e n d s a r e i n d i c a t e d by t h e shaded r e g i o n s which a r e bounded by qmvGaAs f o r l o n g i t u d i n a l a c o u s t i c waves i n GaAs and by qmvAIAs, where vAIAs i s estimated from vGaAs by s i m p l y changing t h e mass d e n s l t y . I n a l l c a s e s t h e d o u b l e t s p l i t t i n g 1s c l o s e t o 2qTSL. The two lower f r e q u e n c y d o u b l e t s a t s m a l l d r e p r e s e n t t r a n s v e r s e modes.

U n c e r t a i n t i e s i n t h e p e r i o d d r e s u l t e i t h e r from n o n u n i f o r m i t y a c r o s s t h e f a c e of t h e sample o r from l a c k of good x-ray d a t a . T h i s p l o t s u g g e s t s t h a t Raman s c a t t e r i n g can be used t o d e t e r m i n e t h e SL p e r i o d o v e r w e l l - d e f i n e d s m a l l r e g i o n s of a sample.

-

d

5

66

2

(I

a,

t 64

62

\

p P '

$

,

-

-

F i g u r e 3 - Folded phonon f r e q u e n c y a t v a r i o u s l a s e r w a v e l e n g t h s i n a SL w i t h

13.9 8 GaAs-11.6 a AlAs.

S o l i d c u r v e i s a l i n e a r c h a i n model c a l c u l a t i o n .

C5-134 JOURNAL DE PHYSIQUE

F i g u r e 4 - Observed f o l d e d a c o u s t i c phonon f r e q u e n c i e s vs. i n v e r s e SL p e r i o d . Shaded r e g i o n s i n d i c a t e f r e q u e n c i e s bounded by b u l k sound v e l o c i t i e s . S q u a r e s i n d i c a t e s a m p l e s w i t h AlAs b a r r i e r s , c i r c l e s r e f e r t o Ale3GaV7As b a r r i e r s .

We n o t i c e i n t h e p l o t of Fig. 4 t h a t some samples show b o t h f i r s t and t h i r d o r d e r f o l d i n g ( i . e . , m = 1,3) b u t no second o r d e r f o l d i n g (m = 2 ) . F i g u r e 5 p r e s e n t s d a t a showing t h i s t a k e n on a sample w i t h 41 8 GaAs - 4 1 8 A10.3Ga0.7As.

0 0

c 0

3 0 F i g u r e 5

-

0 0

U N 41 8 A1 3Ga 7 A s showing m i s s i n g

u second 6rde; f o l d i n g . Data

t a k e n w i t h X L = 5145 8 . ,-

cn 2 0

W 0 - Oo [OOII "/d

2 " X .x,

0 1 I

0 20 40 60 80 100

WAVENUMBER SHIFT

F i g u r e 6 - Raman s p e c t r a a t two l a s e r w a v e l e n g t h s from a n 83 a ^GaAs-90 8 AlS3Ga.7As SL i n (x,x) geometry. I n s e t shows q, f o r p e a k s i n lower c u r v e .

WAVENUMBER SHIFT

COOL1 SCAN

I-

-

29. 0 29. 2 29. 4 29. 6 29. 8 30.

TWO THETA (deS)

F i g u r e 7 - X-ray d a t a f o r s a m p l e of F i g . 6 showing f i r s t t h r e e s a t e l l i t e p o s i t i o n s .

A s e c o n d example i s shown i n F i g . 6 , where t h e l o w e r c u r v e from a 8 3 a ^GaAs-90 a

A10.3Ga0.7A~ sample was t a k e n w i t h X L = 5145 a i n t h e ( x , x ) g e o m e t r y . The m i s s i n g m = 2 o r d e r c a n be e x p l a i n e d by t h e t h e o r y o u t l i n e d below, w h i c h c o r r e l a t e s t h e i n t e n s i t i e s of t h e f o l d e d phonons w i t h s t r u c t u r a l i n f o r m a t i o n . The x-ray d a t a shown i n F i g . 7 shows a l m o s t no m = 2 s a t e l l i t e f o r t h e sample of F i g . 6.

We now s k e t c h a c o n t i n u u m model t h a t a l l o w s a c a l c u l a t i o n of the i n t e n s i t y of Raman s c a t t e r i n g from f o l d e d LA phonons. The s m a l l n e s s of t h e g a p s and t h e l i n e a r i t y of t h e c a l c u l a t e d d i s p e r s i o n c u r v e s s u g g e s t t h a t away from t h e g a p s t h e LA d i s p l a c e m e n t f i e l d c a n b e a p p r o x i m a t e d by t h e p l a n e wave

u ( z ) = uke i k z

w i t h f r e q u e n c y w = CSLk. F o r p h o t o n e n e r g i e s away f r o m i n t e r b a n d r e s o n a n c e s , t h e p h o t o e l a s t i c c o e f f i c i e n t P ( z ) s h o u l d a p p r o x i m a t e l y t a k e t h e form

where x ( z ) i s t h e c o n c e n t r a t i o n of A1 a t d e p t h z i n t h e SL. F o r a n i d e a l s u p e r - l a t t i c e w i t h a b r u p t i n t e r f a c e s P ( z ) w i l l b e a s q u a r e wave, g i v e n o v e r one SL p e r i o d by

P ( z ) = Pa when 0 < z < d l ( 6 a )

~ ( z ) = Pb when d l ( z < d = d l + d2. ( 6 b ) By a n a l o g y w i t h o r d i n a r y B r i l l o u i n s c a t t e r i n g , we assume t h a t t h e s c a t t e r e d i n t e n s i t y o b e y s / 7 /

where f o r l o n g i t u d i n a l s t r a i n s a u / a z L-l L i q z

8 x q = Joe- P ( Z ) [ ~ U ( Z ) / ~ Z ] ~ Z ,

where L is t h e n o r m a l i z a t i o n d e p t h of t h e sample. S i n c e P ( z ) i s p e r i o d i c , we expand i n a F o u r i e r s e r i e s

C5-136 JOURNAL DE PHYSIQUE

and f i n d f o r t h e qth component of t h e o p t i c a l s u s c e p t i b i l i t y

The m = 0 term i n ( 9 ) d e s c r i b e s B r i l l o u i n s c a t t e r i n g a t w = qcSL w i t h i n t e n s i t y

where Po i s t h e a v e r a g e of P ( z ) g i v e n by

The

*

I q

qmlcSL

Using Eq. ( 6 ) t o d e t e r m i n e Pm we f i n d

As e x p e c t e d from F o u r i e r a n a l y s i s of a square-wave when dl = d2 = 112 d , Eq. ( 1 1 ) g i v e s 1, = 0 f o r m even.

When t h e l a s e r photon e n e r g y i s s e l e c t e d t o be n e a r t h e Eo + A, g a p of t h e sample of F i g . 6 , t h e m = 2 and m = 4 p e a k s now a p p e a r , and t h e m = 2 , 3 p e a k s s h i f t t o lower f r e q u e n c y and become asymmetric. Though n o t y e t c o m p l e t e l y u n d e r s t o o d , t h i s b e h a v i o r has s e v e r a l p o s s i b l e e x p l a n a t i o n s . ( i ) I t i s no l o n g e r p o s s i b l e t o d e f i n e a l o c a l p h o t o e l a s t i c c o e f f i c i e n t P ( z ) a s we d i d above f o r t h e non-resonant c a s e . I n r e s o n a n c e one o b t a i n s n o n - l o c a l b e h a v i o r d e t e r m i n e d by t h e r a n g e of t h e SL w a v e f u n c t i o n s i n t h e i n d i v i d u a l quantum w e l l s and between t h e w e l l s . Thus Eq. (11) i s no l o n g e r v a l i d . ( i i ) The asymmetric l i n e s h a p e s a r e p r o b a b l y due t o a n a n t i - r e s o n a n t c o u p l i n g between t h e phonons and a continuum.

The l a t t e r may be s e e n i n Fig. 6 a s a " l a s e r t a i l . " P o s s i b l e c a n d i d a t e s f o r t h e continuum i n c l u d e e l e c t r o n i c s c a t t e r i n g and two-phonon d i f f e r e n c e p r o c e s s e s . I n o t h e r s a m p l e s n e a r a n e l e c t r o n i c r e s o n a n c e we have i n d i c a t i o n s of a n t i - r e s o n a n t b e h a v i o r of b o t h f o l d e d phonons o b e y i n g wavevector c o n s e r v a t i o n and t h o s e from t h e m i n i z o n e b o u n d a r i e s .

0 I I

0 40 00 120 16

WAVENUMBER SHIFT

l i g u r e 8 - Raman s p e c t r a of two SL1s w i t h X L = 5145 a i n ( x , x ) geometry. Upper c u r v e : 12.5 a ^GaAs-37.5 a AlAs.

Lower c u r v e : 37.5 a GaAs- 12.5 a ^AlAs.

A 1 1 t h e Raman r e s u l t s mentioned above were o b t a i n e d on s a m p l e s o f GaAs a l t e r - n a t i n g w i t h A1xGal-xAs where t h e a v e r a g e A1 c o n t e n t was l e s s t h a n 50%. Some

samples have been studied with greater amounts of Al, either by using thick AlAs layers or by adding Al to the GaAs layers. In such samples the Raman data are consistently inferior; the phonon doublets are replaced by broad, often indis- tinct, structures. An example is shown in Fig. 8, where data from two d = 50 A samples are shown, both grown at a substrate temperature of 600°C. The upper curve refers to a sample with 12.5 GaAs and 37.5 A AlAs, and the lower curve to a sample with 37.5 A GaAs - ^12.5 A A1As. No x-ray satellites were found for the former sample. One explanation for the difference between the spectra is an increased layer uniformity and interfacial order caused by the smoothing effect of thicker GaAs layers. /8-9/

In conclusion, we have demonstrated experimentally and theoretically that the Raman spectrum from folded LA phonons contains structural information that correlates well with x-ray diffraction results from (00.8) scans. Raman spectra in higher frequency regions are also affected by superlattice formation, but the changes are subtler and less well understood than those of acoustic phonons discussed here.

We thank T. J. Drummond, J. Klem, and T. Henderson for assistance with sample preparation and T. Gant for help with the Raman measurements. X-ray diffraction measurements were made by H. Zabel, D. Gross and S. L. Cooper in the MRL

microstructure facility. A. C. Gossard provided several small-period samples.

This work was supported by NSF under DMR 82-03523, JSEP under N-00014-79-C-0424 and by AFOSR under F49620-83-K-201.

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7. HAYES, W., LOUDON, R., Scattering of Light by Crystals (Wiley, N.Y., 1978).

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9. DRUMMOND, T. J., KLEM, J., ARNOLD, D., RISCHER, R., THORNE, R. E., LYONS, W. G., MORKOF, H., Appl. Phys. Lett. 42 (1983) 615.