All-Silicon Ultra-Broadband Infrared Light Absorbers

Absorbing infrared radiation efficiently is important for critical applications such as thermal imaging and infrared spectroscopy. Common infrared absorbing materials are not standard in Si VLSI technology. We demonstrate ultra-broadband mid-infrared absorbers based purely on silicon. Broadband absorption is achieved by the combined effects of free carrier absorption, and vibrational and plasmonic absorption resonances. The absorbers, consisting of periodically arranged silicon gratings, can be fabricated using standard optical lithography and deep reactive ion etching techniques, allowing for cost-effective and wafer-scale fabrication of micro-structures. Absorption wavebands in excess of 15 micrometers (5–20 μm) are demonstrated with more than 90% average absorptivity. The structures also exhibit broadband absorption performance even at large angles of incidence (θ = 50°), and independent of polarization.


Optical Characterization
In order to determine optical properties of the highly doped silicon, Drude formalism is used: where ∞ is the permittivity value for >> and taken as 11.7, is the relaxation time, is the plasma frequency: where is the free carrier concentration per cm 3 , is the elementary charge, 0 is the vacuum permittivity, * is the effective mass, and 0 is the electron mass. The procured SOI wafer has n-type silicon layer at the top and p-type silicon layer as the substrate. Resistivity values of these silicon layers correspond to the doping density on the order of = 5 × 10 19 −3 [1]. In order to extract optical properties of both the n-type and p-type silicon layers, we consider plasma frequency and relaxation time as our fitting parameters and we start calculations with = 5 × 10 19 −3 and 1⁄ = 0.037 (eV) [2]. We optimized these parameters by fitting FDTD calculations to our experimental results. Eventually we obtained best fit for = 5.2 × 10 19 −3 and, = 5.5 × 10 19 −3 for n-type and p-type silicon layers, respectively. These carrier concentration values correspond to plasma wavelengths of = 8.28 µ and = 9.42 µ for n-type and p-type silicon layers, respectively. Supplementary Figure S1 shows the modeled real and imaginary permittivity values of our n-type and p-type silicon layers. Supplementary Figure S2 shows the measured, simulated and also analytically calculated (Tmatrix formalism) reflection results of the SOI structure without patterning. In numerical calculations, optical constants of silicon dioxide are taken from the literature [3]. As seen in this figure the numerical and the analytical reflection spectra fit very well to the experimental reflection spectrum indicating validity of our model. Figure S1. Real and imaginary parts of the permittivity for heavily doped n-type and p-type silicon for top and bottom silicon layers of our structure.

Supplementary
Supplementary Figure S2. Measured, simulated and analytically calculated (T-matrix) reflection spectrum of the SOI structure. Inset illustrates the SOI structure.
Highly doped silicon behaves differently at low and high frequencies. In the low frequency regime as ⥲ 0 , 1/ term dominates and imaginary part of the permittivity increases. Thus, at low frequencies, material behaves like a perfect conductor (e.g. a metal). In the high frequency regime 1/ 2 term dominates and imaginary part of the permittivity vanishes. Thus at high frequencies, the optical properties of the highly doped silicon are like those of insulators. Between low and high frequency regimes there is a characteristic transition frequency called plasma frequency at which material's optical response changes from metallic to dielectric. At the plasma frequency, material's real part of the permittivity vanishes, but material's imaginary part of the permittivity is still finite. Around the plasma frequency, since the real part of the permittivity is very low, light can easily penetrate through the material and it is absorbed due to the finite absorption coefficient. Figure S3 shows the bulk absorption of the 4 µm thick silicon with different doping concentrations. As it seen in the graph, absorption peak blueshifts as the concentration increases.
Supplementary Figure S3. Simulated absorption spectra of 4 µm thick silicon with different doping concentrations.

Dispersion relation for different doping concentrations
Simulated dispersion relations of the non-corrugated silicon-silicon dioxide-silicon-air structure for different doping concentrations are shown in Figure S4 (a,b,c). Two vibrational bands of silicon dioxide are at 13.6 THz (22 µm) and 30 THz (10 µm). When the doping concentration is 3x10 20 we can observe an additional absorption band around the plasma frequency. As the doping concentration decreases to 1x10 20 and 5x10 19 the absorption band at plasma frequency region merges with the vibrational band of silicon dioxide. Analytical solution of the dispersion relation for three different concentration are also shown in Figure S4 (d).