Vibrational spectroscopy of periodical semiconductor nanostructures with

quantum dots.

• Introduction• The problem• Results• Conclusion

Mikhail Ladanov

2 2

2 2( ) (1 )LO TO

TO i

0

3

1*

1

3

1 ****

*

h

h

s

s ff

Dielectric function:

Bruggeman effective dielectric function approximation:

IR spectra

Effective dielectric function

Dielectric function of matrix

Dielectric function of QD

*

s

h

IR spectra of AlAs stuctures with QDs

Features corresponded to TO phonons in AlAs QD.

Low freq. shift of TO phonon in respect to the bulk one due to the stress..

There’s no LO phonon peak.

02 .22

22

T

L

SS nn

2

21

1

Basic equationsDielectric continuum approximation:

.,,

,,,

000

0

lmml

ml

mllm

lmmllm

YQQRA

YRA

.1

,2

3,

2

2,

2

1

22/3

12/1!2

,1

,2

1,

2

1,

2!!2

1!2

21

2/2

2

2/2

lmlml

Fl

mlQ

llmlm

Fmll

lR

ml

mmml

l

mlm

ml

Lap. Eq. solution:

(for prolate QD)

1

0

00

lnln

ml

ml

D

Plm R

d

dQ

d

df

,

0

002

2

PlmD

PlmD

T

lm

f

f

Expression for freq. of IF phonons

0 1 2 3 4230

235

380

385

390

l=4l=3l=2l=1

l=4l=3l=2

,

cm

-1

m

l=1

IF phonons in QD. Oblate ellipsoid.

Rp/Re = 1/2

0 1 2 3 4

230

235

385

390

395l=1

l=2

l=3 l=4

l=4

l=3

l=1

l=2

,

cm-1

m

IF phonons in QD. Prolate ellipsoid.

Rp/Re = 2

Freq. of IF phonons in dep. of Re/Rp.

230

240

250

380

390

400

410

(1,1)

(1,0)

,

cm-1

1 101/10

OblateProlate(1,0)

(1,1)

Re/Rp

Experimental Raman spectra of InAs QDs/AlAs (a), AlAs QDs/InAs (b) and InAs QDs/GaAs (c) structures. There’re features between LO and TO phonons freq. which cannot be explained in the frames of 2D structure model for big difference of layers thickness.

Experimental Raman spectra of InAs/AlxGa1-xAs

structures for different x. Spectra, marked with the dotted line, are measured in z(xx)-z scattering geometry, while those, marked with the solid line – in z(xy)-z scattering geometry.

Freq. of IF phonons in InAs/AlGaAs structures

- theory - experiment

ConclusionThe IR reflection and Raman scattering of light by InAs/Al(Ga)As and AlAs/InAs periodic structures with self-organized quantum dots has been investigated. The Raman spectra measured in different scattering geometries exhibit features that correspond to optical TO and LO phonons and interface phonons. The frequencies of TO and LO phonons are displaced with respect to the corresponding values in bulk materials in view of mechanical stresses. The lines of Raman scattering by interface phonons are observed under conditions close to the resonance conditions. The frequencies of interface phonons lie in the spectral range between the frequencies of TO and LO phonons. The experimental frequencies of optical phonons have been used for calculating the frequencies of interface phonons in structures with quantum dots of different shapes in the approximation of a dielectric continuum. The frequencies of interface phonons obtained within this model depend on the shape of the quantum dots. It has been shown that the dielectric-continuum approximation is an adequate model for calculating the frequencies of interface phonons in InAs/AlxGa1–xAs quantum-dot structures with any value of x. In this case, it is assumed that the shape of quantum dots is close to that observed in the spectra obtained by high-resolution electron microscopy. Thus, it has been shown that the Raman spectroscopy is sensitive to the shape of quantum dots.