Introduction
Metamaterials are artificial composite structures which exhibit physical
properties different from the intrinsic properties of the individual
material components (Veselago, 1968). Unusual optical effects such as the
negative refractive index (Shelby et al., 2001) and electromagnetic cloaking
(Schurig et al., 2006) have been observed, which are hardly accessible in
naturally occurring materials (Pimenov et al., 2007). Such properties are
derived from the resonant nature of engineered building units with feature
size smaller than the wavelength of interest. In general, periodically
arranged metal-dielectric structures with unit cell dimensions in the
sub-wavelength regime are employed to independently tune the electric
(Pendry et al., 1996) and magnetic (Pendry et al., 1999) resonances evoked
by the incident radiation. The circulating surface currents induced by
plasmon resonance in the metallic layer accompanied by the displacement
field in the dielectric layer (Dayal and Ramakrishna, 2012) can be manipulated by
changing the geometrical and material parameters. As an effective medium,
metamaterials are characterized by homogeneous parameters such as the
complex effective electric permittivity εω=ε1+iε2 and magnetic permeability μω=μ1+iμ2 (Smith and Pendry, 2006). In research,
much attention has been paid to the real part of ε and μ
to create materials with negative refractive index, while at the same time
minimizing the undesired losses. Similarly, the imaginary loss terms
ε2 and μ2 can be engineered to achieve high
attenuation and consequently large absorption. By independently manipulating
resonances in ε and μ, it is possible to effectively
absorb both the incident electric and magnetic field. Moreover, the
impedance of the metamaterial,Z=εω/μω, can be matched to free space, giving rise to minimized
reflectivity (Landy et al., 2008). The perfect metamaterial absorber (PMA)
is defined to have absorption near unity.
The enhanced absorption properties of metamaterials can be exploited to
tailor the spectral responsivity and selectivity of thermal sensors (Landy
et al., 2008; Maier and Brueckl, 2009, 2010). Thermal sensors such as
bolometer, thermopile, and pyroelectric sensors convert temperature changes
caused by the absorption of incident radiation into an electrical signal.
They usually have a broad spectral response. Exchangeable or fixed optical
filter units are used for wavelength selection. In order to achieve a high
sensor responsivity, a high absorption is required. Therefore, metamaterials
directly integrated on top of thermal sensors are wavelength-selective with
an efficient absorption and optimized heat energy transfer (Maier and Brueckl,
2009, 2010). With the integration of low-mass metamaterials, more compact
and miniaturized thermal devices can be designed without significantly affecting their
response time.
This study focuses on tailoring the optical properties and composition of
micron-sized metamaterial structures based on the requirements arising from
their integration as wavelength-selective PMAs in thermal sensors.
Materials and simulation model
As composite dielectric/metallic materials, highly conductive aluminium (Al)
with low ohmic losses and non-dissipative aluminium nitride (AlN) dielectric
interlayer were chosen. Al is a good thermal and electrical conductor. AlN
has superior thermal and mechanical properties in the infrared. In
particular, the high thermal conductivity of AlN is comparable to metals
such as Al and is compared to Al oxide (Zhao et al., 2004) about 10 times higher.
This is beneficial regarding the heat transfer efficiency to the energy
transducer in an integrated sensor. Moreover, these materials are compatible
with standard microelectronic production processes.
A simple layout of a near-unity absorber mitigates lithographic demands
(Fig. 1). The disc-like top metallic layer (resonator) of an
Al–AlN–Al trilayer is located in the center of the square-shaped unit cell
consisting of the bottom metal and the dielectric layer of side length p.
Due to the circular resonator shape, the excitation of the resonance is
expected to be isotropic and, thus, independent of radiation polarization
(Dayal and Ramakrishna, 2012). As will be discussed later, the trilayer absorber is
additionally extended to a multilayer absorber with alternating
dielectric/metallic stacks (Fig. 1). Moreover, a passivation layer, which is
usually found in thermal sensors – e.g., SiO2 in thermopiles,
Si3Nx in bolometers, or Au in pyroelectric detectors – is also
considered in the layout (Fig. 1). The disk radius in the unit cell
determines the areal density of the metamaterial.
Schematic illustration of the unit cell in the numerical
simulations.
Finite-element simulations based on the commercially available software
package COMSOL Multiphysics were performed to analyze the optical properties
of a reduced three-dimensional model (Fig. 1). The incident light is an
electromagnetic plane wave propagating at normal incidence along the
negative z direction. The boundary conditions for the unit cell outer walls
perpendicular and parallel to the electric field are a perfect electric and
perfect magnetic conductor, respectively. For the top and bottom outer walls
scattering boundary conditions with and without an incident wave are used,
respectively. The experimental refractive index values of the individual
materials including the dispersion relation are taken from Kischkat et al. (2012), Ordal et al. (1985), and Palik (1985) and implemented in the model. The
field distributions, and the time-averaged power flow in the structure is
calculated. Reflection is determined by simulating the same elementary cell
geometry with all layer domain properties set to vacuum and normalized to
the incident intensity. The difference in the integrated power flow at the
individual layer boundaries reveal the absorption values as Aω=1-R(ω)-T(ω), with the frequency-dependent reflectance
R(ω) and transmittance T(ω).
Simulation results
Electric and magnetic resonances
The incident electromagnetic plane wave propagating in negative z direction
excites plasmon resonances in the top metallic layer, and thus polarization
currents depending on the electrical permittivity appear inside the metal.
The resonator layer at the top behaves like an electric dipole that serves
as a coupler to the electric field of the incident wave. Consequently, the
electromagnetic fields are concentrated within sub-wavelength regimes
leading to a significant increase of the local field strengths (Fig. 2a).
The origins of magnetic resonances are antiparallel currents in the metallic
layers, which, together with the displacement field in the dielectric layer,
result in circulating currents (Dayal and Ramakrishna, 2012; Tao et al., 2008). The current loop
induces a magnetic dipole moment that can resonantly couple to the magnetic
field vector of the incident light. For a strong localization of the
electromagnetic energy within the metamaterial, both an electric and a
magnetic dipole resonant coupling at the same frequency are necessary. This
resonant coupling is of destructive nature for the reflected direction, thus
eliminating reflection. In a PMA, neither reflections nor transmissions of
the incident light at a given wavelength can be observed (Pendry et al., 1999;
Zeng et al., 2013).
Optical properties of metamaterials for simultaneous electric and
magnetic resonances. (a) Normalized electric field and (b) magnetic field.
(c) Surface current density. (d) Time-averaged energy flow defined by the
Poynting vector. (e) Volume-averaged energy flow (z component) over the
spectral range of interest.
The simulated electromagnetic field distributions within the absorber
element where both resonances appear are exemplarily shown in Fig. 2. Here,
typical geometric parameters for resonator radius and thickness, dielectric,
bottom metal, and SiO2 substrate thicknesses are 500 and 50, 110,
150, and 250 nm, respectively. The distribution of the electric field in
Fig. 2a shows the typical dipole excitation and spatial localization within
the dielectric interlayer. The concentration of the magnetic field in the
dielectric layer demonstrates the confinement of the magnetic field caused
by the oscillating current loop (Fig. 2b). The inhomogeneous distribution
of the current density in both metal layers is depicted in Fig. 2c. For
smaller wavelengths in close proximity to the resonance, the surface current
density displays a rather homogeneous distribution with significantly lower
current magnitudes. By approaching the resonance wavelength, the current
density experiences a progressive increase at the outer center of the
resonator and reaches its maximum value at resonance wavelength. For
wavelengths beyond the resonance, the current density steadily decreases.
It is noteworthy that the surface current reverses its sign from positive to
negative, resulting in a directional change of the circulating current loop.
The normalized current density magnitude is slightly asymmetric for
wavelengths smaller and larger than the resonance wavelength. The induced
image charges in the bottom metal layer behave similar to those observed in
the top metal layer. The current sheets in the bottom layer are antiparallel
oriented and show slightly lower amplitudes compared to the top layer. In
agreement to theoretical predictions, the current sheets in both metallic
layers form a circulating current loop, have comparable amplitudes, and are
slightly out of phase (Dayal and Ramakrishna, 2012; Zeng et al., 2013). For wavelengths far from
the resonance, the whole resonant structure acts like an ordinary material
with a current density behavior according to its intrinsic characteristics.
Figure 2d displays the corresponding time-averaged energy flow of the
electromagnetic wave in the absorber element at resonance. The energy flows
from the outer border towards the center of the resonator. The energy flow
in minus z direction averaged over the entire unit cell volume demonstrates
the wavelength-dependent energy transfer. At resonance wavelength, an
enhancement energy transfer by a factor of about 25 is observed (Fig. 2e).
Trilayer absorbers at normal light incidence
The absorption behavior of circular-shaped trilayer resonators with regard
to their geometrical design is discussed. The angle of radiation incidence
is 90∘, i.e., normal incidence. First, the influence on the
optical properties by varying the lateral dimensions as well as the layer
thicknesses of the resonator, dielectric, and the bottom metal layer are
presented. Moreover, the effects arising from changes in the substrate layer
thickness and material as well as the resonator density or filling factor
are discussed.
Figure 3a shows a selection of absorption spectra for resonator radii
varying between 275 and 600 nm, while all other parameters were kept
constant. The layer thicknesses of the resonator, dielectric, bottom metal,
and SiO2 substrate are 50, 115, 50, and 250 nm, respectively. The
unit cell side length is 2.1 µm. A variation of the resonator radius
results in a clear shift of the resonance peak, which indicates a change in
the effective dielectric permittivity of the metamaterial structure. The
resonance wavelength experiences a linear red shift with increasing radius.
According to a linear fit, a radius change of 10 nm causes a shift in the
resonance wavelength of 80 nm. This is a good reference value in order to
estimate peak shifts due to variation in the size of the absorber element,
i.e., geometric tolerances caused by fabrication errors. The full width at half
maximum (FWHM) of the absorption peak gives information about the coupling
strength of excited oscillations in the metamaterial system. There is a
linear dependence on the resonator radius ranging from 275 to 600 nm with
FWHM values of 100 and 700 nm, respectively. The observed peak broadening
is due to a gradual increase of dissipative losses in the metamaterial.
Numerical calculations of absorption spectra for varying (a) resonator
radius, (b) dielectric layer thickness, and (c) resonator (hre) and
bottom metal (hbm) thickness.
Figure 3b presents the calculated absorption properties for varying
dielectric thicknesses between 30 and 210 nm, while all other parameters
remain constant: resonator radius and height, bottom metal and substrate
thicknesses, and unit cell length are 525 and 50 nm, 50 and 250 nm,
and 2.1 µm, respectively. A change in the dielectric thickness
influences primarily the inductance or magnetic resonance and, thus, the
effective magnetic permeability of the absorber system. A varying dielectric
thickness also affects the capacitive coupling to the bottom metal layer,
i.e., it changes the effective permittivity, but in a less pronounced manner.
Basically, lower layer thicknesses result in higher capacity and lower
inductance of the system and vice versa. The resonance frequency remains
constant at a resonance wavelength of 4.5 µm in a broad thickness
range of 70–210 nm (Fig. 3b). This behavior reflects the relation of the
resonance frequency (ω0) to the capacitance (C) and inductance
(L) of the structure, which can be considered as an undamped resonant
circuit:
ω0=1LC.
For dielectric thicknesses below 70 nm, there is an imbalance between the
inductance and capacitance of the structure, which results in a significant
red shift of the resonance along with a reduction in the amplitude. This
behavior is characteristic for a damped oscillation. Figuratively speaking,
a steady decrease of the dielectric layer thickness means a gradual approach
of the antiparallel-oriented magnetic fields in the resonator and
bottom metal layer generated by the two corresponding antiparallel-circulating
current loops. For large dielectric thicknesses, an antiparallel
orientation of the magnetic fields is energetically favored. A steady
decrease of the dielectric layer leads to an increased perturbative
interaction. As a consequence, the magnetic fields could perform precession
motions when the dielectric thickness falls below a critical value
(∼ 70 nm). A precession means a distortion of flow of the
current loops compared to the case for larger dielectric thicknesses. A
change in the current flow can be considered as an additional inductance
source. The total inductance (L=Lg+Lp) of the structure is then
the result of the geometrical inductance (Lg) and the inductance
induced by current perturbations (Lp). Due to the additional
perturbative losses, the magnetic resonance frequency does not solely scale
up with the geometrical inductance (Lg). By introducing an effective
damping factor to Eq. (), both a shift of the resonance frequency and a
reduction of the amplitude can be explained. However, at very thin
dielectric thicknesses, the direction of the magnetic field of the
bottom metal layer flips and aligns parallel to the upper resonator magnetic
field due to energy minimization reasons. In this configuration no magnetic
resonances occur, and the absorption properties are determined by the
materials permittivity. The calculations show that the amplitude reaches its
maximum value of 0.96 at a dielectric thickness of 110 nm and decreases for
larger and smaller layer thickness values similar to a negative parabolic
function. The absorption remains within the range 90–130 nm around 0.9. The
FWHM value of about 475 nm is lowest at a thickness of 110 nm, and it remains
within the range of 90–130 nm almost constant. Smaller or larger layer
thicknesses result in a FWHM increase up to 950 nm.
In a PMA, the layer thickness of both the resonator and the bottom metal
needs optimization. The penetration depth of an electromagnetic wave into a
metallic layer and, thus, the transmission T(ω) is determined by
the wavelength-dependent skin effect. If the thickness of the bottom layer
is smaller than the skin depth, image charges are not effectively formed in
the bottom metal layer, deteriorating the magnetic resonance. This also
implies a dielectric dipole resonance without a proper impedance
matching. Therefore, an effective energy transfer is hindered, and unwanted
reflections might occur (Dayal and Ramakrishna, 2012). The resonator (bottom layer)
thickness range of 30 to 150 nm (30 to 200 nm) was analyzed. The results
shown in Fig. 3c are calculated for 525 nm radius, 110 nm dielectric
height, 250 nm substrate height, and 2.1 µm unit cell length. For all
investigated thickness permutations, the absorption remains always larger
than 0.9 and reaches the near-unity absorption value of 0.995 for the pair
combination of 50 nm resonator thickness and 150 nm bottom metal thickness.
The position of the resonance peak remains constant for all combinations.
The FWHM has a slightly oscillatory behavior within the range of 495 ± 25 nm.
Thermal detectors are capped for instance by insulating layers such as
SiO2, Si3Nx, or conductive Au layers. Their influence on the
absorption of integrated metamaterials is also investigated in the
simulation model (Fig. 1). In all simulations up to here, a
SiO2 substrate of 250 nm was assumed. SiO2 thickness variations up
to 3 µm show no noticeable changes in the absorption behavior (data
not shown). In the case of a gold passivation layer variation (30 to 200 nm), a slightly decreased absorption within the range of 50 to 110 nm
from near unity to 0.95 could be observed. Since the transmission T(ω) in this metamaterial structure is negligible, the marginal absorption
deviations can be explained by changes in the image charge formation in the
bottom layer and energy flow direction affected by the conductive Au layer.
The resonator density or filling ratio, i.e., resonator base surface area
compared to the elementary cell base surface area, affects the absorption. A
resonator density of more than 50 % is required for high absorption
values, while a decreasing absorption is observed for smaller values (data
not shown). Similar to our previous studies (Maier and Brueckl, 2009, 2010), there is
no indication of coupling between the absorber elements down to a lateral
absorber-to-absorber distance of 600 nm. Thus, for distances larger than 600 nm
no influence on the resonance frequency could be observed. Due to the
short-range nature of the lateral field distribution at resonant frequency
(Fig. 2a and b), coupling phenomena occur typically at distances of about
half the resonator diameter.
Trilayer absorbers at oblique light incidence
Conventional thermal detectors usually respond to a broad spectral range of
the incident radiation. A wavelength-selective response is achieved by
implementing exchangeable optical filters or microfilters in front of the
detector. Such filters possess an angular transmission characteristic and
show a limited selective performance above a critical angle of incidence.
Here, the angular dependence of the absorption of metamaterial structures
are simulated based on the transmission line model. Similar geometric
parameters are chosen: the individual thicknesses of the resonator,
dielectric, bottom metal are 50, 110, and 150 nm, respectively, with a
resonator radius of 500 nm.
Absorption properties for TE and TM polarization at oblique angle
of light incidence.
Multilayer absorption spectra for (a) trilayer, (b) one-stack, and
(c) two-stack systems. (d) Dual-band absorber based on a modified one-stack absorber.
All insets show the specific stack configurations. (e) and (f) represent the
electric and magnetic field distribution in the absorber at different
resonance wavelengths related to absorption spectra shown in (b) and (c),
respectively.
For transverse-electric (TE) or transverse-magnetic (TM) polarized light at normal incidence, both the electric and
magnetic field are aligned parallel to the resonator plane and are
represented by the corresponding in-plane field components. If we consider
the case of TE or TM polarization at oblique light incidence, the respective
in-plane component of the electric or magnetic field remain unchanged, while
the respective in-plane magnetic (Hip) or electric (Eip) field
component parallel to the resonator plane decrease with incidence angle
α as Hip=H0cos(α) and Eip=E0cos(α), with
H0 and E0 being the corresponding field magnitudes at normal
incidence. In contrast to normal light incidence, we obtain at oblique
radiation incidence additional out-of-plane field components (Hop,Eop)
perpendicular to the resonator plane, which increase with incidence
angle according to Hop(Eop)=H0(E0)sin(α). Figure 4
illustrates the angular dependence of the TE and TM mode of the incident
radiation with the electric and magnetic field aligned parallel to the long
semi-axis, respectively. For both TE and TM polarized light the absorption
remains higher than 0.94, and a slight shift in the resonance wavelength can
be observed up to an angle of incidence of 40∘. For the TE mode
even 85 % of the intensity is absorbed at an angle of 60∘. The
overall nonlinear decrease reaches 45 % absorption at 80∘.
Remarkable for the TE mode is an unchanged resonance wavelength for all
angles with a steady nonlinear decrease in the absorption. Characteristic
for the TM mode is the high (> 90 %) absorption up to an angle
of 60∘. With rising angle, a slight decrease in the intensity of
absorption is observed accompanied by a resonance shift of
11 nm/∘
to smaller wavelengths. Due to Eq. (), a shift in the resonance wavelength
is expected when the inductance and/or capacitance of the systems changes. A
gradual angle increase is comparable to a tilt of the resonant structure
relative to the incident direction of the electromagnetic wave, and the
initial circular shape of the resonator gradually becomes elliptical. This
shape transformation from circular to elliptical leads to a decrease of the
resonator surface area with increasing angle of incidence. This in turn
effectively reduces the capacitance of the resonator which results according
to Eq. () in a shift of the resonance to smaller wavelengths. However, this
implies for TE (TM) polarization a higher impact on the magnetic
(electric) resonances, depending on whether the electric or magnetic field
is aligned parallel to the resonator plane at all angles. In case of the
TE mode, the constant remaining in-plane electric field ensures even at high
angles of incidence a continual resonant coupling and, thus, plasmon
excitation, while the steadily decreasing in-plane magnetic field leads to a
gradual magnetic decoupling. As a consequence, the resonance frequency
remains constant, while the amplitude decreases nonlinearly with increasing
angle of incidence due to magnetic losses. In contrast to the TM mode, the
electric losses caused by a successive decoupling of the in-plane electric
field with the angle of incidence result in a nonlinear peak broadening and
decrease in absorption (Fig. 4). These findings are also supported by an
additional simplified simulation approach considering anisotropic resonators
at normal light incidence (data not shown). In this approach, a modulation
of the shape from initially circular to elliptical was investigated. The
short semi-axis is varied, while the long semi-axis remains constant and
corresponds to the initial radius. A linear decrease of the short semi-axis
with the electric field oriented parallel to it results in a clear linear
resonance shift to smaller wavelengths, while the amplitude remains almost
unchanged. For the antiparallel-oriented electric field, a clear amplitude
decrease without significant alteration of the resonance frequency is
observed. Although the results of the two approaches are not one-to-one
transferable, they still share some common basic properties and help to
qualitatively interpret results or to recognize tendencies.
Multilayer absorbers at normal light incidence
A multilayer system with additional dielectric/metallic layers stacked on
top of the resonator disc is studied. These disc-shaped, alternating
metal and dielectric layers have thicknesses of 50 and 100 nm, respectively.
Note that an n-stack system represents the trilayer system with n additional
AlN–Al stacks on top of the resonator. The following simulation parameters
remain constant during the calculations: resonator radius and height,
dielectric, bottom metal, and SiO2 substrate height are 500 and 50, 115, 150, and 250 nm, respectively. The absorption spectrum of a
zero-stack system in Fig. 5a corresponds to the trilayer system at resonance
frequency and serves here as a reference. It shows a near-unity absorption
at a resonance wavelength of 5.19 µm with a FWHM value of 650 nm, and
the respective maximum electric (magnetic) field value is 29.04 V m-1 (0.0728 A m-1). Characteristic for the absorption behavior of a one-stack system is a
spectral peak broadening with a FWHM value of 1050 nm, which is due to the
excitation of a second resonance at 4.85 µm and its superposition
with the absorption peak of the trilayer at 5.19 µm (Fig. 5b). The
absorption peak at 4.85 µm results from a resonant coupling of the
incident light mainly in the upper stack, which is indicated by the
concentration of the electric and magnetic field in the upper circular
dielectric layer (Fig. 5e). A steady increase of the wavelength leads to a
gradual localization displacement of both fields, resulting in a dominant
field concentration in the dielectric of the trilayer at the wavelength of
5.19 µm. Compared to the plain trilayer system, both resonances
feature a marginally weaker coupling of the electric and magnetic field, which
leads to slightly lower absorption peaks. The difference in the excitation
frequency arises from lateral geometrical differences. The reduced metallic
area in the first stack might result in confined surface currents leading to
two different effective permittivities and permeabilities. The calculated
resonance peak in a two-stack system basically represents the superposition of
three different resonances (Fig. 5c and f). The first, second, and third
resonances appear at wavelengths of 4.83, 4.97, and 5.19 µm, respectively. Similar to the one-stack system, they are due to a
main localization of the electric and magnetic field in the top, middle
dielectric layer, and the dielectric of the trilayer (Fig. 5f). For
comparison, the maximum electric and magnetic field magnitudes of the third
resonance are comparable to those calculated in the plain trilayer and
one-stack system. In contrast, due to a less efficient electromagnetic
coupling the respective maximum electric (magnetic) field values of the
first and second resonance are about 38 % (30 %) lower, which lead to
an overall nonlinear absorption decrease. Therefore, the peak of the third
resonance is well pronounced compared to the first and second resonances,
while the spectral peak broadening is still comparable to that observed in a
one-stack system. Since the two disc-shaped stacks in the two-stack system hold
the same geometry and consist of the same materials, one would expect the
first two corresponding resonances to appear at the same wavelength.
However, the decisive difference between them lies in their respective
boundaries, which are defined by the adjacent layers surrounding the top and
the middle stack. The top stack is sandwiched by air and the adjacent layers
of the middle stack. Besides the interaction with the top stack, the middle
stack is additionally influenced by the underlying trilayer, which finally
leads to a slight resonance shift of about 0.14 µm. In contrast, the
resonance wavelengths due to field localizations in the top dielectric layer
remain almost constant for the one- and two-stack system (Fig. 5e and f). It
should be noted at this point that, so far, only the geometrical parameters
of the trilayer system have been optimized towards perfect absorption.
Further optimizations by tuning the geometrical parameters of the disc-shaped
stacks could minimize unwanted reflections of such multi-stack
systems leading to highly efficient electromagnetic coupling at distinct
wavelengths. This can result in multiple resonances with perfect absorption
as exemplarily demonstrated in the following section for the one-stack system.
A modified design of the shown one-stack system was optimized toward the
realization of a wavelength selective “perfect dual-band absorber” (Fig. 5d). The tailored radius of the top disc is 350 nm, while the radius of the
underlying dielectric and metallic layer is 575 nm. Except for the radii, all
other parameters remain identical. In accordance to Fig. 3a, two absorption
peaks appear at a resonance wavelength of 3.0 and 5.0 µm
for absorber radius 350 and 575 nm, respectively, although the disks are
stacked in this case. The absorption for both spectral bands reaches values
very close to unity (> 99.9 %). The electric and magnetic
resonance properties display similar characteristics to the unmodified
zero-stack metamaterial structure. As a consequence, a “perfect multiband
absorber” can be designed by combining n-stack systems consisting of
n resonators of different size (Dayal and Ramakrishna, 2013).