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# Control of the degree of infiltration

Specular reflectance measurements allow us to follow the growth process and determine the CdS content, f, by fitting

the positions of the first stop band at L point through Bragg law. To estimate

f we have linearly interpolated the dielectric constant of the composite. It

is important to point out that, for later inversion, CdS content has to be as

high as possible. Figures close to the available volume in the bare matrix,

which is 26% for a compact face centred cubic (fcc) structure, are needed. This

is a strong requirement if a self-standing inverse CdS structure is to be

produced. Experimental results from reflectance measurements as a function of

incidence angle can be seen in Fig. 1 for a sample of 275 nm diameter spheres

subjected to different treatments with increasing reaction times. CdS contents

of about 3%, 9%, 16%, 32%, 42%, 80% and 96% relative to the pore volume are

found. Absolute infillings, f, are indicated in the labelling. In

addition, data from the initial bare opal are shown. Let us not forget that the

kind of characterization obtained by this means is macroscopic, the size of the

probing beam being much larger than the microscopic features of the sample. This

is particularly important for the highly infiltrated samples and means that high

infill figures do not stem from local aggregations of CdS but from a uniform

loading. Two important conclusions can be extracted from these data. First and

most important: it is possible to infiltrate to almost 100% of the free volume;

second: on loading, the composite keeps all of its photonic properties

associated with the fcc arrangement along (111) direction.

FIG. 1 Bragg peak position for bare and different

CdS loaded opals of 275 nm spheres. Symbols represent experimental data and

solid lines represent the fits to Bragg law.

We have studied the behaviour of

the L gap edges as the infiltration degree increases and both the dielectric

contrast and the topology of the (more strongly) scattering matter change. The

main finding is that the gap to midgap ratio decreases from about 6% in the

original opal (f = 0) to about 3% in half loaded structures (f ≈

0.1) and then increases to ca. 12% for full infiltration while the gap centre

steadily decreases following the increase in average dielectric constant of the

composite. Fig. 2 shows the band edges at L point versus the CdS filling

fraction (from 0, bare opal, to 0.26, fully infiltrated). Circles represent

experimental data and lines theoretical predictions. Experimental data are

obtained by plotting the energies, on either side of the peak, where reflectance

takes on one half of its maximum value. The photonic band structures were

obtained by solving the corresponding differential equation for electromagnetic

wave propagation using a plane wave basis in an iterative implementation. In

order to simulate the dielectric distribution two semiconductor growth modes

were considered. The first model (dotted line in Fig. 2) maps a homogenous

distribution of dielectric constant in the opal voids (with increasing value for

increasing CdS content). The second one (continuous line in Fig. 2) assumes a

layered growth such that the CdS forms shells that surround the opal spheres. An

increase in CdS fraction means, in the first model, denser material filling the

opal voids while, in the second one, thicker coating of the spheres. The first

model is proposed because the very early stages of the CdS growth, as

microscopic characterization shows, starts by forming nanometric grains in the

space left by the silica spheres leading to a silica opal in which a mixture of

CdS and air fills the pores. The second growth mode was observed for Si in this

sort of open structures.

FIG. 2 Experimental L point stop band edges

for the opal-CdS composites (circles) and theoretical predictions (lines).

Homogeneous distribution model (dotted) and coating layer model (solid). Top

axis shows, in percentage of the sphere radius, the layer thickness for the

latter.

In the early stages, the CdS growth seems to

proceed by a shell thickening route (continuous line in Fig. 2). This behaviour

is, on the other hand, the only mechanism expected at very low infilling since

new grains can only be formed on the surface of the spheres or on previously

formed grains.. For higher infiltrations (f >0.1), it is difficult to

precise which mode is followed because of data scattering but clearly, the

initial behaviour is abandoned. This might be explained as follows. At first,

grains of CdS nucleate on the spheres surface and cover the silica sphere in a

layered growth. When the reaction time is longer a CdS network fills the opal

voids, and small pockets of air are left empty. In this way, only very long

exposures to the reactants can lead to a complete infiltration of the micropores.

Another interesting feature that can be extracted form Fig. 2 is that, in the

homogenous model, the stop band at L vanishes when the average dielectric

constant of the loaded voids (background) coincides with that of the silica (es=2.1)

spheres and the composite becomes optically uniform. This can be written as

epore=1+f/0.26·(eCdS-1),

where eCdS=5.75.

Equating epore

to the silica dielectric constant yields f=0.06, very close to the value

obtained from full theoretical calculations based on the first model (f=0.055).

At this point, the dielectric contrast disappears and, consequently, no photonic

crystal effects are expected. In the layered growth model, however, this cannot

happen because of symmetry considerations: there cannot be 4 degenerate states

in an anisotropic medium. At any rate, the fact that, for any filling ratio, the

materials have precise boundaries and preserve the periodic structure at the

relevant wavelength scale impedes the cancellation of dielectric contrast: an

optically uniform medium is never obtained by increasing the thickness of the

CdS layer. Notice that, as can be seen in Fig. 2, very thin layers are needed to

achieve sizable infillings. The top axis presents the layer thickness for the

corresponding filling ratio in units of the sphere radius. For instance at

filling ratios less than 10% the CdS layer is thinner than 5% of the radius

which means, in practical terms, a few nanometers. This further supports the

assumption that even in the case where growth is based on the formation of

grains, the growth can only begin by a coating of the spheres

.

FIG. 3 SEM image of a (111) facet from a 275 nm

spheres CdS inverted sample. The channels left by the sintering and through

which the HF flows can be seen. The inset shows a lower magnification image

where the overall structure is viewed.

Once nearly full CdS infiltration has been reached,

the inversion of the structure can be tackled with all guaranties. To do that,

the CdS/opal is immersed in a 1% diluted HF solution for about six hours. For

the success of this operation, it is very important that silica spheres are in

contact with each other in order that HF flows throughout the structure. This

requirement is fulfilled in sintered samples with a filling fraction of 0.74. By

this procedure, macroscopic samples have been obtained in which optical

measurements are performed. Fig. 3 shows a typical SEM image of a (111) internal

facet of CdS inverse opal (sphere diameter 275 nm) after cleavage. In the inset,

the uniformity of the growth and that very high percentage of infilling achieved

(virtually 100%, yielding a negative replica of the original opal) can be

appreciated.

FIG. 4 Reflectance at 10 degrees incidence (solid

lines) angle and theoretical position of the first stop band at L point (dashed

areas) for a 275 nm spheres opal.

Optical properties of the samples thus

obtained have been explored by means of reflectance (taken, for practical

convenience, at 10 degrees incidence) and compared with those of the original

bare opal and infiltrated one. The optical characterization of this type of

structures is not extensive in literature because macroscopic, high quality

samples are needed. In Fig. 4 the reflectance at 10 degrees incidence for a 275

nm sphere opal in its three stages (bare, CdS infiltrated to 96%, and inverted)

is plotted. Dimensionless units of a/l

are used. The shadowed areas represent the predicted

photonic pseudogap at L point. Theoretical estimates are for bare opal (top),

fully infiltrated (middle) and totally inverted (bottom). The agreement between

theory and experiment is satisfactory. Starting from bare opal (Silica-air), the

gap to midgap ratio for this first pseudogap is about 6% with a refractive index

contrast of 1.45; in the CdS-Silica composite, the ratio is 12% and the contrast

1.7; finally, for the inverted structure, the ratio is 18% the contrast being

2.4. The increase measured in the final structure (three times with respect to

the initial opal) is a huge enhancement of the photonic properties and very

useful for systems in which a strong interaction is needed between the photonic

structure and an active material therein. In the case of CdS, the semiconductor

itself is the active material.