Germanium inverse opals by CVD

Germanium inverse opals by CVD

Germanium is infiltrated by CVD
by using digermane (Ge2H6) as a precursor. First, opal
templates are introduced in a cell in which a high vacuum is made (5x10-6
torr). Then, the cell is cooled with liquid nitrogen and the germanium
precursor, Ge2H6 gas, is let to fill the line and reach
the sample. The low temperature of the reactor gives rise to the condensation of
the Ge2H6 inside it, the gas pressure being varied between
300 torr and 1000 torr. After, the reactor is heated up to a temperature at
which the decomposition of Ge2H6 takes place to give Ge
and H2. The range of temperatures employed was 473 K<T<623 K. In each
case, the temperature was kept constant for 21 hours.

A structural analysis of the
Ge-SiO2 composite performed by scanning electron microscopy (SEM)
reveals that the growth takes place layer by layer, which gives rise to a
uniform shell coating of the silica spheres. So, the occlusion of the external
pores is prevented (see figure 1A). This treatment also allows a homogeneous
infiltration along the whole silica template, as was checked by observing the
fractured edges of the samples (see figure 1B). The germanium coating thickness
was measured in the images and, therefore, the percentage of infiltration
estimated. This can be controlled by varying the Ge2H6
pressure and the deposition temperature. In general, within the range of
temperatures we employ, higher Ge2H6 pressure results in a
thicker germanium coating.

Finally, the inverse opal was
finally obtained by removing the silica opal. Samples were introduced in a 1% HF
in water solution during 48 hours. The connectivity of the silica template,
caused by sintering, allows the acid solution to flow all through the structure
as the silica is etched. By this procedure, we obtain a germanium inverse opal
which has inherited the long range FCC order of the original template. The
presence of windows interconnecting the spherical cavities reflects the necks
between the particles in the template (see figure 1(D)).

Under the conditions described above,
amorphous germanium is synthesised, as it was confirmed by X-ray diffraction (XRD)
and Raman spectroscopy measurements. In order to crystallise it, the samples
were annealed at 773 K. The effect of the crystallisation process on the Raman
spectrum is shown in figure 2. The broad and asymmetric Raman shift peak
observed at 270 cm-1, characteristic of amorphous germanium,
displaces to 298 cm-1, which corresponds to the G25
phonon in crystalline germanium. The symmetry and the narrow bandwidth (Dn=13
cm-1) of the latter indicates the absence of nanocrystallites in the coating.
This result is in good agreement with the analysis of crystal size from the XRD
patterns. These clearly show peaks corresponding to the diamond-like structure
of germanium.

Figure 1. (A) SEM image of the external
surface of a 1.2 mm spheres opal infiltrated of germanium by CVD (Ge2H6
pressure, P=490 torr; decomposition temperature, Td=523 K). The layer
by layer growth gives rise to a uniform germanium coating of the spheres, that
prevents the occlusion of the external pores. (B) SEM image of a cleaved edge of
a germanium infiltrated opal (1.2 mm spheres, P=930 torr, Td=573 K).
Fracturing the samples allows to measure the germanium coating thickness (70 nm)
and to confirm the uniform infiltration through the whole template. (C) and (D),
SEM images of internal surfaces of a germanium inverse opal (spherical cavity
size 1.2 mm,
P=930 torr, Td=573 K). (A) Detail of a {111} type plane in which the
germanium walls (70 nm) left after the silica etching are shown. (B) {110} type
surface. The large windows interconnecting the spherical cavities are due to the
sintering of the opal template.

Figure 2. Raman spectra of
germanium infiltrated opals as-grown (dotted line) and after annealing at 773 K
(solid line). Even at the highest Ge2H6 decomposition temperature employed (623
K), the amorphous phase of germanium grows on the spheres surface.

The photonic crystal behaviour of the samples
at each step of the fabrication process was studied by optical reflectance
measurements in the near infrared. Samples were illuminated with unpolarised
light under a microscope so that the spot size (40 mm x 40 mm) was smaller than
the observed typical domain size, the incident light cone spanning 15º to 35º
from normal incidence with respect to the (111) planes (G-L direction) of the
sample. A Bomen’s Fourier transform infrared spectrometer was employed to
perform the spectral analysis of the reflected light.

Germanium infiltrated opals present wide, well
defined reflectance peaks at low energy, corresponding to the first photonic
stop band that opens at the edge of the first Brillouin zone in the G-L
direction. These peaks are shown in figure 3 for a germanium infiltrated silica
opal made of 1130 nm diameter spheres for two different germanium coating
thickness. The reflectance spectrum of the original silica template is also
shown. It can be seen that the optical properties strongly depend on the degree
of infiltration, a huge red shift being observed for the germanium infiltrated
opals. This is a consequence of the increase of the average dielectric constant
after infiltration. Another remarkable feature is the broadening of the peak due
to the increasing of the dielectric contrast in the structure. Experimental gap
to midgap ratios are Dl/l=14.5%
(dashed line) and Dl/l=17%
(solid) for the infiltrated opals while Dl/l=6%
for the silica template (dotted line). The reflectance spectra of the
infiltrated samples also shows several intense peaks at higher energy, which has
been removed from figure 3 for the sake of clarity. The evolution of the size
and position of the lowest optical gaps observed in the infiltrated opal showed
good agreement with theoretical calculations (see details below). Hence, they
could be employed to monitor and control the degree of infiltration before the
etching takes place.

Figure 4 shows the reflectance spectra of the
inverted structures resulting from the etching of the infiltrated opals shown in
figure 3. When compared, we can see that the first stop band at the L point
moves towards shorter wavelengths when the silica is removed. Also, it widens up
to Dl/l=16%
(dotted line) and Dl/l=21.5%
(solid line), as a result of the higher dielectric contrast of the inverse
structure. When comparing the optical spectra of inverse opals with different Ge
filling fraction values, it has to be noticed that, in despite of the complexity
of the spectra, the number of peaks (five) and their shapes are the same in both
inverted structures. Only the position and width vary as a result of the
different degree of infiltration (filling fraction). It demonstrates that a fine
tuning of the photonic band gap behaviour can be achieved by controlling the
germanium layer thickness growth in the CVD process.

Figure 3. Normalised
reflectance spectra for a sintered bare opal made of 1130 nm spheres (dotted
line), and the same opal infiltrated of germanium. The dashed line corresponds
to a germanium filling fraction of ff=58% of the opal void volume (Ge coating
thickness: 45 nm). The solid one, to ff= 78% (Ge coating thickness: 70 nm).

On the basis of the data
obtained from the SEM characterisation (lattice parameter, degree of sintering,
and Ge coating thickness), we calculated the photonic band structure of the FCC
germanium inverted structures fabricated. These calculations were done employing
2662 plane waves, the dielectric constant being sampled at 512x512x512 points in
the FCC primitive unit cell. We observe that the size of the windows
interconnecting the hollow spherical cavities, determined by the degree of
sintering, or a small change of the degree of Ge infiltration can completely
modify the band structure at high energy. This strong dependence with the fine
structure of the PBG material is particularly important since a full gap is
expected to open between eighth and ninth bands for germanium inverted opals.

Figure 4. Reflectance spectra
of the germanium inverted structures obtained from the SiO2-Ge opals whose
optical properties are shown in figure 3. The optical features of the resulting
hollow material can be tuned by changing the germanium CVD conditions. An
asterisk highlights the peak corresponding to the full photonic band gap, after
the theoretical calculations (see figure 5).

Results presented in figures 3
and 4 correspond to samples with a lattice constant a=1580 nm and a sintering
factor of sf=a0/a=1.01 (a0 and a being the
lattice constant of the opal template before and after sintering respectively).
Ge refractive index was taken to be n=4.1. Our calculations predict that
germanium inverse opals with such characteristics will show a full gap for a
filling fractions higher than 61%, which in our case corresponds to a Ge coating
thickness of 47.5 nm. Therefore, only the inverted opal with a thicker coating
(70 nm) is expected to present a full band gap. The photonic band structure for
such inverted opal is presented in figure 5. All the photonic gaps that open at
the G-L
direction, the one we test in our optical reflection experiments, are shaded.
Only the full gap, at 2 mm,
is shaded along every crystalline direction plotted in the graph. We can
establish a clear correspondence between all the peaks observed experimentally
and the calculated photonic band gaps along G-L.
This comparison indicates that the third reflectance peak (at around l=2.1 mm, indicated
with an asterisk) in the solid line spectrum in figure 4 corresponds to a full
photonic band gap in the inverted opal. A good agreement is also found between
theoretical and experimental full photonic gap to midgap ratio, those being 8.6
% and 6.5% respectively. As light impinges the samples slightly deviated from
the G-L
direction, reflectance peak widths and positions are slightly different from
those extracted from figure 5. Although the results shown here indicates the
opening of a full PBG, a thorough optical analysis of all crystalline directions
should be done to confirm it and will be a matter of future research.

Figure 5. Photonic band structure of a
germanium (n=4.1) inverted opal obtained from a sintered SiO2 opal (sf=a0/a=1.01)
whose void lattice was infiltrated up to a 78 % of its volume (Ge coating
thickness: 70 nm). A full photonic band gap opens at a/l
=0.8. a0 and a: lattice parameter of the structure before and after sintering.