Chapter 4 Raman Spectroscopy of GaAs in Si Nanotrenches
4.4 Theory of Raman scattering
According to G. Irmer [32], for long-wavelength polar phonons in the cubic crystal
classes the Raman scattering efficiency is given by
2
phonons p are expressed in the principal crystallographic axes system as denoted by
strokes. The Raman tensor R of the phonons with symmetry Γ
( )
F in crystals ofthe point group T has the form d
( )
Rij k(4.2) with one independent element a which is a measure of the changes of susceptibility
with the phonon displacement.
Consider the zinc-blende (001) facet. In the backscattering configuration, the TO
phonon has the polarization p=
(
px,py,0)
, with incident light polarization at <110>direction and scattered light polarization at <110> direction, the Raman scattering
efficiency is calculated to be zero. With the same condition, the LO phonon has the
polarization p=
(
0,0,pz)
and the Raman scattering efficiency is calculated to be 2apz,meaning allowed in this configuration.
To explain our experimental results of the large TO mode, since our work has done
with the z(XX)z’ configuration, the only parameter changed should be the Raman tensor.
The values of the Raman tensor are based on the symmetry of the lattice. In our case,
we consider that the micro-twins in the micro-crystals would change the symmetry of
(001) facet, which cause the large TO signal.
In the nano-trenches, there is an additional mode between TO and LO mode. This
mode is attributed to the “surface phonon” (SO) mode due to a large surface-to-volume
ratio. With the calculation of R. Ruppin et al. [33], SO phonon has three main
characteristics:
(a) The SO mode is locate between the bulk TO and LO peaks.
(b) The SO mode shifts to lower frequency as the dielectric constant of the
surrounding medium increases.
(c) The intensity of the SO mode increases as the particle size decreases.
The SO mode is fitted when the trench width is less than 100 nm. No obvious trend
can be seen in figure 4.5 and 4.6.
Figure 4.1 (a) RT Si (100) bulk z(XX)z’ 1second 2cycle (b) RT VPEC GaAs (100)
z(XX)z’ 30 seconds 2cycle (c) RT C2584 (100) bulk z(XX)z’ 30 seconds 2 cycle (d) RT
C2584 (100) bulk z(yX)z’ 30 seconds 2 cycle (e) P. A. Temple et al. [31]’s result (b)
(d) (c)
(a)
(e)
Figure 4.2 (a) C2585(100) bulk z(XX)z’ 30 seconds 2 cycle in log scale (b) C2585 (100)
bulk z(yX)z’ 30 seconds 2 cycle in log scale (c) C2585(100) bulk z(XX)z’ 30
seconds 2 cycle GaAs signal in linear scale (d) C2585 (100) bulk z(yX)z’ 30
seconds 2 cycle GaAs signal in linear scale (c)
(b) (a)
(d)
Figure 4.3 (a) C2586 Si (100) bulk z(XX)z’ 30 seconds 2 cycle in log scale (b) C2586
Si (110) bulk z(yX)z’ 30 seconds 2 cycle in log scale (c) C2586 Si (100) bulk
z(XX)z’ 30 seconds 2 cycle GaAs signal in linear scale (d) C2586 Si (110)
bulk z(yX)z’ 30 seconds 2 cycle GaAs signal in linear scale (b)
(d) (c)
(a)
Figure 4.4 (a) C2587 Si (100) bulk z(XX)z’ 30 seconds 2 cycle in log scale (b) C2587
Si (110) bulk z(yX)z’ 30 seconds 2 cycle in log scale (c) C2587 Si (100)
bulk z(XX)z’ 30 seconds 2 cycle GaAs signal in linear scale (d) C2587 Si
(110) bulk z(yX)z’ 30 seconds 2 cycle GaAs signal in linear scale (b)
(d) (a)
(c)
Figure 4.5 (a) C2588 GaAs in 40nm trench 30 seconds 2 cycle Raman spectrum in
linear scale with Lorentzian fitting (b) C2588 GaAs in 45nm trench 30 seconds 2 cycle
Raman spectrum in linear scale with Lorentzian fitting (c) C2588 GaAs in 50nm trench
30 seconds 2 cycle Raman spectrum in linear scale with Lorentzian fitting (d) C2588
GaAs in 55nm trench 30 seconds 2 cycle Raman spectrum in linear scale with
Lorentzian fitting (c)
(a) (b)
(d)
Figure 4.6 (a) C2588 GaAs in 60nm trench 30 seconds 2 cycle Raman spectrum in
linear scale with Lorentzian fitting (b) C2588 GaAs in 70nm trench 30 seconds 2 cycle
Raman spectrum in linear scale with Lorentzian fitting (c) C2588 GaAs in 80nm trench
30 seconds 2 cycle Raman spectrum in linear scale with Lorentzian fitting (d) C2588
GaAs in 90nm trench 30 seconds 2 cycle Raman spectrum in linear scale with
Lorentzian fitting
(a) (b)
(c) (d)
Figure 4.7 (a) C2588 GaAs in 100nm trench 30 seconds 2 cycle Raman spectrum in
linear scale with Lorentzian fitting (b) C2588 GaAs in 120nm trench 30
seconds 2 cycle Raman spectrum in linear scale with Lorentzian fitting (c)
C2588 GaAs in 140nm trench 30 seconds 2 cycle Raman spectrum in linear
scale with Lorentzian fitting (d) C2588 GaAs in 160nm trench 30 seconds 2
cycle Raman spectrum in linear scale with Lorentzian fitting
(a) (b)
(c) (d)
Figure 4.8 (a) C2588 GaAs in 180nm trench 30 seconds 2 cycle Raman spectrum in
linear scale with Lorentzian fitting (b) C2588 GaAs in 200nm trench 30
seconds 2 cycle Raman spectrum in linear scale with Lorentzian fitting (c)
C2588 GaAs in 300nm trench 30 seconds 2 cycle Raman spectrum in linear
scale with Lorentzian fitting (d) C2588 GaAs in 500nm trench 30 seconds 2
cycle Raman spectrum in linear scale with Lorentzian fitting
(a) (b)
(c) (d) (d)
Figure 4.9 (a) The trends of TO phonon, SO phonon and LO phonon in variant trenches,
respectively. (b) The trends of FWHM of TO and LO phonon, respectively.
Chapter 5 Conclusion
We have successfully deduced the theoretical formation origin of the anomalous
spectra of 300 nm GaAs on planar and patterned Si (001) substrate. From the
observation of SEM images of GaAs on Si (001) bulk spectra, we believe that the RTCL
peak broadening is due to the band gap overlap of the strained grain. From the
observation of C2588 GaAs on patterned Si (001) substrate, we conclude that the ultra-
broaden 1.45 eV peak is attributed to the GaAs band to band luminescence and the 1.29
eV shoulder is attributed to the Si deep level luminescence. The LTCL GaAs peaks
reveal a two-peak feature when trench width between 90 nm and 140 nm. The low
energy band is attributed to deep level carrier to carbon acceptor and the high energy
band is attributed to donor to acceptor recombination, respectively.
The origins of three SiO2 RTCL peaks are also surveyed. The 1.9 eV peak is
attributed to the NBOHC; the 2.2 eV peak is attributed to the (VO;(O2)i) structure and
the 2.7 eV peak is attributed to E’ center. From the observation of LTCL, we find out
that the elimination of 2.7 eV and 2.2 eV peaks, which represents the elimination of
these defects. In the analysis of GaAs on planar Si, the basic two peaks at 1.32 eV and
1.47 eV are attributed to the deep level transition and the GaAs band to band transition,
respectively. The other bands are attributed to the Fermi-level consistency inducing
band gap changing of strained grains.
The RT Raman spectra are studied. Large originally forbidden TO mode was
observed in the z(XX)z’ configuration of GaAs on planar Si (001) substrates. The large
TO mode is attributed to the large density of the micro-twins, which transform the (001)
facet to the {122} facets. The same as the planar Si (001) substrates, the patterned Si
(001) sample shows large LO phonon mode. Additionally, the surface optical (SO)
phonon mode is observed in the trenches thinner than 100 nm. The SO mode is due to
the large surface-to-volume ratio.
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