Inelastic light scattering from strained-layer SiGe superlattices

Superlattices

and Microstructures,

INELASTIC

LIGHT

717

Vol. 4, No. 6. 1988

SCATTERING W. Bacsa,

FROM

SI/GE

II. v. Kane& K. A. Milder, M.Ospelt

Laboratorium

fiir FestkBrperphysik, (Received

We have studied

STRAINED-LAYER

strained-layer

ML) Ge layers by inelastic

Si/Ge

light (Raman)

and P. Wachter

ETH Honggerberg,

CH 8093 Zurich

1 June 1988)

superlattices scattering.

(SL) composed

order have been observed

in the growth strain.

direction.

The observed

indicating

abrupt

The energy of the optical shift is consistent

of ultrathin

The SL’s with periods

27 to 72A have been grown on Si (100) by MBE. Folded longitudinal to the fourth

SUPERLATTICES

interfaces

(3-6

ranging

acoustic

from

phonons

up

and exellent uniformity

modes of the Ge layers is shifted due to

with the calculated

value obtained

using uniaxial

stress parameters.

1. Introduction With

the advent

MBE and MOCVD (SL) composed successful

the fabrication

of different

endeavour.

a reduction

of artificial

affect the propagation

the constituent

leads to

neither

in the growth

are formed

Inelastic

back of the dispersion

light scattering

both for lattice

terised by a rather by using Si,Ger_, G. Abstreiter

alloy layers.

nari ’ have shown theoretically superlattices

can be derived

Ge, the corresponding perlattice pounds. overlap. of Si. reduced

throughout

phonon

In

of Si and

region of the bulk com-

branches

But those of Ge overlap The corresponding amplitudes

materials.

branches

the entire superlattice.

mainly in the acoustic

The optical

properties

of pure Si and Ge layers

dispersion

modes

The various

at the

coinciding

with

modes are thus a measure

periodicity

(extended

modes)

Recently,

modes),

the indi-

and the interfaces

the experimental

Si/Ge

superlattices

become

possible

superiattices

realisation

consisting s.

(interface

by inelastic

of short

period

of pure Si and Ge layers has

In the following

with periods

we report

on Si/Ge

in the range between light (Raman)

30 to 70A,

scattering.

2. Experimental The [loo] oriented, been cleaned

of Si and Ge do not

n-type

Si-wavers to 830°C

them to a small Si-flux. In addition

prepared

exhibit

in this manner

reconstructed

from a Knudsen

respectively.

exceeding

Our Si,Ge,

during

superlattices

systems

x

2)

beam

is lo-“mbar,

are grown

not

9. First, the thickness

at temperatures

rates of about

both Si and Ge. There exist two critical to be kept below the critical

1+ 1

Ge and Si have

growth.

with evaporation

ones

Substrates x

cell and an electron

The base preassure

10-‘Ombar

of 460 - 480°C

growth

(2

surface as verified by RHEED.

been evaporated gun,

a smooth

have

and by

a buffer layer

was grown at 700°C.

have

phonons

annealing

of 500 - 1OOOA thickness

of the superlattice The optical

(0.05-5Rcm)

in situ by thermal

with the acoustical

in the Si layers.

07494036/88/060717+05$02.00/0

force constants

modes).

subjecting

folded phonon modes of the Si/Ge su-

can propagate

This happens

et aL5 and

Fasolino and Moli-

from those of the constituent

the energy range of overlapping

modes.

Si and Ge

how the phonon

consisting

being ex-

The bonds

those of Ge nor those of Si. They give rise to local-

investigated

such Si - S&Gel_,

light scattering.

lead to different

ized phonon

can be reduced

D.J. Lookwood

et al6 have investigated

in the Ge layers.

are charac-

of 4% between

This large mismatch

by inelastic

acousmatched

lv2) and for strained-layer

large mismatch

at room temperature.

damped

for the superlattice

curves of

by folded longitudinal

has been reported

GaAs - Al,Gal_,As

superlattices

may

edge of Ge and are therefore

to the Si layers, their amplitudes

vidual layers (confined

In particular

SL’s (e.g. GaSb - AZSb 3,4). Si/Ge superlattices

of Si/Ge

which

materials.

tic (LA) phonons SL’s (e.g.

periodicity

planes

the phonon

confined

interface

of waves in the crystal.

by the folding

strictly

ponentially

superlattices

modes arise which to a first approximation

be described

as

a highly

zone dimension

new Bragg

such

has become

The superlattice

As a result,

new phonon

techniques,

materials

of the Brillouin

direction.

of Si are beyond

of new growth

of an individual

thickness

of Ge on Si. Experimentally

0.5A/s

thicknesses

for

for such

Ge-layer

has

h, for pseudomorphic h, has been found to be

0 1988 Academic Press Limited

Superlattices

‘La) 10 2i.4

and Microstructures,

Vol. 4, No. 6, 1988

All the ohstbrvc,d L.4 doublets

(fig.3b).

SIIC)V.I!

symmctrj-.i.e. they only appear for parallel polarisatiolr rertions

of the incident

is to be expected modes

and scattered

nal acoustic

branch

in backscattering phonon mension,

acoustic

branch

(symmetry

:11,

fl,) are Raman-allow%

from the [OOl] face.

q with respect

alters the selection

The observed I

I

100

I

I

200 inelastic shift

I

t

400 [cd]

folded LA phonons

FIG. 1. Overview

spectrum

of the investigated

SL 230.

model i-6.

as an elastic continuum.

perlattice.

the lattice

to neglect

the microscopic

Solving the wave equation

lation is obtained in the range of 6 monolayers

s. Second,

the total

superlattice

must

strained

the critical assume

thickness

the latter

S&,Ge,

layer

at which strain

with n = 3 - 6 monolayers a total thickness thickness,

Backscattering

200mW laser.

scattering

The penetration

backscattered computer

light

at this wavelength

of the superlattice

controlled

double

HG 2 S). The resolution hers, and the samples

is about The

was analyzed

monochromator

was set between

(Jobin

by a Yvon

4 and 8 wavenum-

were kept in a helium atmosphere

to

^.._1..>. I” 1^... ^.._:r_r:__^‘ _c nr2 _-2 tLxLlllUt: W *___..___.. ,leque’LLyCX.clbdLI” “ LD I 1’ *u” II “2. 3. Results Figure

1 displays

and

spectrum

period

of 5OA. The average

between

4 and 5 monolayers.

tic phonon fourth

obtained

from a Si/Ge thickness

They

are sharp

with Si layers in this thickness region features

superlattice

At low energies,

of the bulk materials associated

range. there

with a

in the acousdoublets

up to

for all samples

In the optic phonon

appear

with a mode largely

light scat-

of the Ge layers was

and intense

rc-

- k&c,)]

three prominent

confined

to the Ge

z =

velocities

and Q = 2 ( y

index of refraction denote

bulk com-

tion (1) describes

period

respectively.

the folding

of the momentum

Ge (i = -0.15). to equation

densities

as obtained

from the linearity

to equation

The superlattice the experimental

(1). In table I we compare

superlattices

n/m,

obtained

near the

(1). As input i.e. the rela-

of Ge and Si in the superlattices by fitting

from

of the folded LA phonons

very well by equation

from RBS data.

then determined

It originates

6 in the two layers

This effect is small for Si and

(1) we have used the ratio

tive thicknesses

dispersion

The second term describes

The frequencies

(fig. 1-3) are described

of

The first term in equa-

the layering effect on the linear dispersion.

boundaries.

in vacuum;

and the thicknesses

back of the linear

medium.

re-

n(Xo) is the

at X0, the laser wavelength

of a continuous

Brillouin-zone

densities,

) the wave vector;

the superlattice

the Si and Ge layers, relation

in the corresponding

pi and p; the mass and momentum

spectively d,di

Si,Ge

PSl - PGe

6 =

and yields gaps and deviations

region of Si and Ge we observe

order.

Vi are the sound

pounds,

the difference

Discussion

an overview of the inelastic

tering

elastic

dispersion

+ kdc.)

Pivi

u=PSi+PGe

by

thickness.

P* =

vi

and the total

line of an argon

the superlattice

k, 1 ”

with

we used 80mW-

and 488nm

depth than

cos(qd)= $$ncos(I;szds,

(1)

+ 6 sin(k&si

(RBS).

experiments

power of the 514nm

68OOA and is larger

We

have been determined

Spectroscopy

for longitudinal

the following

It

of the sty

superlattices

up to 18OOA. The ratio n/m

For the light

occurs.

and m = 19 - 50 monolayers

and hence the period,

Rutherford

structure

lo:

of the corresponding Si,Ge,

alloy 7. We have fabricated

wavelength

in this region.

thickness not exceed

relaxation

to be equal to that

in

the lattice can bc

The phonon constant

waves in an infinite superlattice

of a Si,Ge,

may be analysed

of bulk Si and Ge (0- lOOcm-‘)

is reasonable

1.0

“.

In the linear region of the

dispersion

than

zone di-

rules of the folded phonons

considered

is much longer

The finit<,

to the Brillouin

those of a zone center mode with Al symmetry terms of a continuum

(syrnnrr

and those from the longitutli

geometry

momentum

(11

‘l‘his behav~o~i

t hrory ‘: The zonr r~rrtor

from group

folded from the transverse

try 1;) arc Raman-forbidden

light.

Si,Ge,,

periods

were

peak positions

the periods of several

by this procedure

with those from the

layers, one strictly confined to Si and an interface mode in l...r..._.._ rl^+“:l_A ..: ^..I “1 ,.*+I.,. .%“,...^+:““^-:-., “CLWCC,,&L_ 1UCA_..^ IIW”. fi* -^_^ ,II”IC UCCaUCU “,CV? bI,c:‘ &.c”UUIIIL IC&jl”II

RBS analysis. The agreement is quite satisfactory, the Ra-^_ “aba A”*- 1-..>:-,, f^ ,._-._...l..,r Urg‘ l.:_l..... T_ rl._ ^” lllall IrTIIU1‘1& I,” D”LLLC*vlla(l lrl .._1..__ “CUUlz5.111 Lllr ..__ upp?z,

of the spectra

parts

is shown in figure 2 and 3. The results

spond to superlattices

with periods decreasing

corre-

from 72i (fig.

of figure 2 and 3 are displayed

(eq.(l)).

A collection

of the data

the dipersion obtained

relations

for the various

Superlattices

and Microstructures,

0 FIG. 2. Inelastic

160 inelastic shift [cc11

light scattering

719

Vol. 4, No. 6, 1988

6

260

spectra from SL 233 (a) and SL

232 (b). The upper parts of the figures show the disper-

2 10

160 inelastic shift [cs ‘I

sion relation momentum

SL and photon

(1) for the corresponding q.

c 1

0

0

200 100 inelastic shift

inelastic shift FIG. 3. Inelastic

light scattering

spectra

of SL 246 (a) and SL

249 (b). The upper parts of the figures show the disper-

SL’s is shown in fig.4. positions mension folded

are plotted r/d

phonons

In this figure the expected

as a function

(full lines).

of the Brillouin

sion relation momentum

&I

(1) for the corresponding

SL and photon

q.

doublet

case of the dots the unresolved

zone di-

tained

from a least-squares

frequencies

of the

From the upper horizontal

by dots and squares.

In the

d in A a measure

The observed

are indicated

I

I

I

doublet

fit employing

separation Gaussian

was obprofiles.

scale in fig.4 giving the SL period

of the sensitivity

of the Raman

effect to

720

Table

Superlattices ctnergy hi&

I superlattice

period

relatiw

thickness

230 :

of the

t,hesr excitations higher

sample nulnbe~:

and Microstructures,

doublet

first

1t.M [A]

RBS [Si/Ge]

close to the p = 0 values calculated

48.5

50.5

0.88/0.12

the folded TA dispersion

232 :

53.7

52.5

O.R7/0.13

that

72.6

72.1

O-88/0.12

ter diverges

0.88/0.12

the origin of the observed

44.8

41.9

246 :

30.9

248 :

27.4

23.9

0.75jO.25

249 :

26.9

24.2

0.7s/0.25

a density

of states

iutensitich

The eu~rgics are

Even though

effect might excitation

be involved remains

The optical phonon

region of the hulk materials

peak (A) at 315cm-’

(B) on its low energy around

28A (SL 249) already

suffices for the doublet

ration

to be no longer visible due to the broadening From the present preparation

control)

a roughness

has to be accounted of the interfaces tensity

of the order for. Another

procedure

of the acoustic

briefly on the additional

250

FIG. 4. Folded doublet 2

= E

70

phonon

regions

positions

6CI

energies

denote

strain

50

in reciprocal

The measured

thicknesses positions

The biaxial

(fig.5).

i.e. for a strain

investigated

between are dis-

of 4.2%.

from [loo] only the

determined

can be calcu-

of pseudomorphic

The latter

corresponds

of SL 246 (11.4cm-‘)

25 [Al

30

played by full squares displayed

,4l

by uniaxial

to

The shift of peak (A) is the same for all

SL’s with the exception

resolved doublets);

in t,hc

at r into a

with the observed

under the assumption

a stress of 50 kbar.

strain

splits the triplet

In backscattering

of

shoulder

shift of peak (A)

l2 the shift of the singlet

40

space.

strain

is shown

is composed

to the biaxial

Using parameters

experiments

growth,

The upward

active in accordance

lated to be 16~~’

on the low

side.

and a singlet.

symmetry

of the in-

the range of the expected

for the relative

and $j$.

(1.5d)

ll. Before ending the

which appear

at

correspond-

with a pronounced

can be attributed

singlet is Raman

we would like to comment

excitations

?O

acoustic

The shaded

range,

doublet

of the

of the sharpness

is given by the weak dependence

on the order m of the doublets

discussion

Ge layers.

sepa-

(no RHEED

of one monolayer indication

by 15cm-’

of 1.7A

peaks.

that

unexplained

in more detail in fig.5 for SL 230. The excitation a sharp

An uncertainty

(the la-

present.

0.81/0.19

in d can be obtained.

of

it appearh

we have to concede

ing to the LO mode in pure Ge (300~7~‘)

fluctuations

rl~~’

for the first doublc(

relation.

at the zone center),

cI

I-he synrmcrr\

period.

t,he superlattice

R.WlKXll

233 : 241 :

(lig.2,3).

The corresponding

is Al.

the smaller

Vol. 4, No. 6, 1988

(resolved

doublets)

those calculated

by open rectangles.

and dots (un-

according

to (1) are

Superlattices

and Microstructures,

721

Vol. 4, No. 6, 1988

acterised

the strained-layer

Si/Ge

Si(100) by MBE. The uniformity the sharpness

of the interfaces

in the monolayer growth

range.

on and

of pseudomorphic

from the strain

observded

in

Ge-layers.

Acknowledgement M. Elmiger perimental

grown

have both been found to lie

The persistence

has been established

the ultrathin

superlattices

of the SL-periodicity

-

for critical aspects

Swiss National

We wish to gratefully

discussions

of this work.

Science

thank

on theoretical Financal

Foundation

and ex-

support

(NFP

by the

19) is gratefully

acknowledged.

I 250

350

References

inelastic shift [crri ‘1 FIG. 5. Ge-like optical

phonons

B are explained

1. C. Colvard,

in SL 230, shifted by strain.

Phys.Rev.Lett.G,298

A,

2. J. Sapriel,

in the text.

R. Merlin, M.V. Klein, and A.C. Gossard,

J. Kerverec,

periods

(40).

relaxed due to the large number

The persistence

of pseudomorphic

our SL’s has been verified by high resolution (B) (fig.5) present 14 In between

the optical

at 415cm-‘. strain

mode which we have to associate (fig.1).

with Si-Ge

mode has been

for all SL’s; again with

relaxed

SL 246, where it is

Hence this mode too shifts upwards although

upon lowering

to 488nm, indicating

by approximately

Ge mode.

optic modes the intensity

plete account

This interface

418 - 420cm-’

of the partially

of the lower-lying nificantly

modes of Si and Ge we observe

By contrast

of the interface the excitation

resonance

of this feature

with in-

half the amount to the other mode increases

wavelength

enhancement.

two sig-

from 514

A more com-

will be given in a subsequent

4

and W.A. Sunder,

4868 (1987)

P.V. Santos,

A.K. Sood, M. Cardona,

Phys.Rev.m,

and K. Ploog,

6381 (1988)

5. H. Brugger

and G. Abstreiter, jj&

5928 (1986)

6. D.J. Lockwood,

M.W. Dharma-wardana,

J.M. Baribeau,

and D.C. Houghton

Phys.Rev.

2243 (1987)

jj&

7. A. Fasolino

to appear

in Journal

8. J. Bevk, J.P. Mannaerts,

de Physique

L.C. Feldman,

B.A. Davidson,

A. Ourmazd, Applied

Physics

Letters

9. R. Hull, J.C. Bean, Gibson,

Applied

10. M. Rytov,

Akust.

11. M.V. Klein, Journal

99, 283 (1986)

F. Cerdeira,

Physics

Letters

A.T. Fiory a,

Zh. 2,71 (1956)

C. Colvard,

de Physique

12. F. Cerdeira, 4. Conclusion

R. Fischer

vol $& colloque

we may state:

tering as a highly versatile

using inelastic

C.J. Buchenauer,

and M. Cardona, light scat-

tool, we have quantitatively

char-

13. L. Tapfer,

Phys.Rev.

to be published

14. to be published

and J.M.

56 (1986) and H. Morkoc, C5, pp.

1984.

publication.

In conclusion

G.J. Gualtieri

Phys.Rev.&j&

Phys.Rev.

found to lie between

creasing

elsewhere

2007 (1983)

3. G.P. Schwartz,

in

X-ray diffrac-

in all samples will be presented

bonds at the interface the exception

growth

l3 An extensive discussion of the shoulder

tion experiments

an additional

of

R. Vacher,

and A. Regreny,

Phys.Rev.&& which may have partially

(1980)

J.C. Michel, J.C. Tolbano,

F.H. Pollak 6, 580 (1972)

131-137,