2.1.

Fabrication of Optical Structures

Porous Si samples were prepared from single-crystal, (100)-oriented highly boron-doped p-type Si (Siltronix, Archamps, France, 0.92 mΩ cm resistivity) by electrochemical etching in a 3:1 v:v solution of aqueous hydrofluoric acid (HF) to ethanol (49% hydrofluoric acid from Fisher Scientific, Inc., Pittsburgh, PA, USA). Etching was performed in a Teflon^® cell with a platinum mesh counter electrode and a galvanostat (Kepco, Inc., Flushing, NY, USA, BOP 50–4D) under computer control (LabView, National Instruments, Austin, TX, USA). Single- and composite-frequency rugate etches were fabricated with a current waveform varying between 25 and 100 mA/cm², applied nominally for 45 cycles with other sinusoid conditions as indicated. Fresh HF was introduced to the etch cell during electrochemical fabrication by replacing 1.5 mL of the 3:1 etch solution at 5-min intervals. Lifted-off porous films for use in FTIR transmission mode were achieved by detaching the porous layer from the bulk Si wafer with an electropolishing current of 2.7 mA/cm² for 5 min in a 3.3% HF:ethanol solution. Rugate etch currents varied as a function of time t, according to

2.2.

Gravimetric Determination of Porosity

Samples were weighed before etching (m₁), after etching (m₂), and after dissolving the porous layer with a 0.1-M basic solution of KOH in water and rinsing with ethanol (m₃). The following equation was used to determine the porosity:³⁰

2.3.

Infrared Spectroscopy

Spectra were recorded with a Thermo Scientific Nicolet 6700 FTIR with an MCT/A detector and KBr beam splitter using a resolution of 2 cm⁻¹ and an average of 128 scans. Attenuated total reflectance (ATR) spectra were acquired with a smart iTR diamond accessory. Transmission-mode spectra were acquired by mounting the lifted-off porous Si film between two KBr circular plates (Koch Crystal, Elyria, OH, USA) and placing the assembly on a transmittance accessory stage normal to the infrared beam. Reflectance-mode spectra were acquired with a beam-deflector setup as pictured in Fig. 1 and with filters that were not lifted off from the bulk underlying Si. Four Ag mirrors (Thorlabs, Newton, NJ, USA), mounted on posts and positioned at a specular angle of 12.5 deg, diverted the beam path through a gas sample cell. The 2.5-in-long glass gas cell was positioned in the beam path as depicted and used KBr windows and had Swagelok input and output ports. Reference spectra were taken by replacing one mirror, on the detector side of the gas cell, with polished Si. Sample spectra were taken by replacing the polished Si with a porous Si sample. A flow of ∼2 L/min of nitrogen, measured with a mass flow controller (Alicat Scientific, Tucson, AZ, USA) was passed through the gas cell. Spectral acquisitions with CO₂ were taken by first purging the cell with a 2-L/min flow of CO₂ for 5 min, with continuous flow during sampling.

Fig. 1

Schematic view of the reflectance-mode gas-sensing configuration used. The source and detector are from a conventional FTIR instrument. Silver mirrors divert the beam (arrows) through a gas cell with KBr windows. The porous silicon optical structure (pSi) is mounted at one of the beam-deflection locations, as pictured. A reference spectrum is acquired with a polished silicon chip mounted in the pSi location.

2.4.

Effectical Optical Thickness Determination

Reflectance spectra of the samples in the visible region were taken across 530–1200 nm with a CCD spectrometer (Ocean Optics, Dunedin, FL, USA, USB4000) and a tungsten-halogen light source (Ocean Optics LS-1) connected with a Y-branch bifurcated optical fiber. The common end of the bifurcated fiber was focused with an objective lens to a 2-mm² spot size and positioned normal to the porous silicon sample surface. A routine using a fast Fourier transform (FFT) of the optical interference fringes in the visible between 850 and 1000 nm was used to determine the effective optical thickness (EOT) (2 nL) of the layers.³¹

2.5.

Scanning Electron Microscopy

Porous silicon layer thickness was determined by cutting and imaging cross sections of the filters with an FEI XL30 SFEG scanning electron microscope (SEM) in ultra high-resolution mode with a through lens detector at 10 kV without prior metallic sputtering of the sample.

3.1.

Porous Si Rugate Filters with Medium-Wavelength Infrared Spectral Features

A comparison of spectra from three FTIR acquisition configurations for a filter with a sinusoidal current-time waveform period of p = 60 s is shown in Fig. 2. In all configurations, spectral bands corresponding to the filter material are observed. The filters in this study were designed with resonant peaks outside of the bands corresponding to the Si–H vibrational signatures of the freshly prepared filters. Oxidation of the filters by aging in air will introduce spectral bands corresponding to Si–O and Si–OH bonds that must also be avoided. Spectra obtained in the ATR configuration clearly exhibit features of the fresh Si–H surface, with ν(SiH_x) stretches at 2112 and 2087 cm⁻¹, δ(SiH₂) at 907 cm⁻¹, and δ(SiH_x) at 623 cm⁻¹. No rugate stop band feature is visible under ATR due to the limited depth of penetration of the infrared beam into the filter layer relative to the physical thickness of the rugate cycles.

Fig. 2

Comparison of three FTIR acquisition modes and resulting spectra for an infrared rugate optical structure with a sinusoid etching wave period of 60 s. (a) Attenuated total reflectance. (b) The optical structure was lifted off from the bulk and the spectrum acquired in transmission mode. (c) Reflection-mode interrogation using the beam diversion configuration in Fig. 1. The percent reflectivity is relative to a polished Si reference sample.

In the transmission configuration, the ν(SiH_x) stretching vibration is very strong, since the light is absorbed in that band as it passes through the optical film. The principal rugate band at 1715 cm⁻¹ is observed, as well as higher order harmonics at 2/λ and 3/λ.⁴ If desired, these higher order harmonics may be suppressed by creating filters with a sinusoidal modulation of the logarithm of the refractive index n with depth^{3, 18} rather than a direct sine variation of n. Here, the 2/λ band was desired and utilized as an optical reference channel. The thickness of the filter balances a trade-off between increasing the number of sinusoid repetitions to reduce thin-film interference fringes and increasing the material's absorbance in the Si–H bands outside of the desired rugate spectral position.

To sense absorbing molecules in the beam path, a reflection rather than transmission configuration is desirable. In reflection mode, an absorbing gas is sensed as a reduction in peak reflectivity, while in transmission mode the absorbing gas results in a slight decrease in the already low filter transmittance of the rugate band. The spectrum in Fig. 2 obtained in the reflection configuration clearly exhibits the rugate reflection band as well as higher order harmonics at 2/λ and 3/λ, with the Si–H stretches of the material's absorbance appearing as reductions in the reflectivity at ∼2100 cm⁻¹. Thin-film interference fringes are present due to reflections from the top and bottom interfaces of the optical structure, where the bottom interface consists of the porous Si layer and bulk silicon. Despite mounting the porous Si sample at a 15-deg angle of incidence, the center wavenumber of the rugate band at 1742 cm⁻¹ in the reflectance configuration was only slightly lower than its appearance at 1730 cm⁻¹ in the transmission configuration, where the filter was normal to the incident beam. This is not surprising because, for an incident angle θ₀, the wavelength of the peak at an angle θ relative to its location at normal incidence (λ₀) is given by:¹²

3.2.

Effect of Rugate Repetitions

Increasing the number of sinusoid etch repetitions for a given fixed period reduces the height of the thin layer interference fringes relative to the rugate peak while increasing the etch thickness. Thicker layers result in increased absorption at porous Si–H absorption frequencies.

For the gas-sensing work above, layers with 45 rugate cycles were chosen as a nominal value exhibiting acceptable thin-film fringe reduction. Figure 3 displays spectra taken in reflectance mode of four etches with varying numbers of rugate cycles for a period of p = 43.7 s. The effective optical thickness (2n_avgL) increases linearly with the number of cycles due to the linear increase in the layer thickness L, for the constant average layer refractive index n_avg. This result indicates that issues affecting the etch rate of the porous layer do not dramatically deviate the linearity of the optical thickness with total etch time for very thick (>50 μm) etches.³² Specifically, the diffusion of the HF electrolyte into the increasingly thicker film during long etches does not appear to have limited the etch rate.

Fig. 3

(a) Effect of the number of sine wave cycles on the reflectivity spectrum, for an optical structure with a period of 43.7 s. (b) Linear relationship between the effective optical thickness (2n_avgL, determined from the interference fringes apparent in the visible portion of the reflectance spectrum), and the number of sine wave cycles.

3.3.

Effect of the Etching Period

The period of the current-time etch wave, given in Eq. 2, corresponds directly to the spectral position of the rugate band, and rugates with spectral bands across the MWIR have been created. Figure 4 displays reflectance FTIR spectra of several of these filters.

Fig. 4

Comparison of a series of etches with constant total etching times but with (a) a variable number of cycle repetitions to a series of etches with a constant number of sinusoid cycle repetitions but (b) with variable etching times. Spectra from structures of four of the sine-wave periods in each series are shown. The total etch time was equal to the period times (in seconds) the number of cycles. The two calibrations coincide at p = 50 s, where each consisted of 45 repetitions and a total etch time of 2250 s.

The periodic variation of the current density with time given in Eq. 2 results in a periodic variation of the refractive index with depth z, expressed as^{3, 4}

Figure 4 compares two sets of period versus peak wavelength (λ₀) calibrations of MWIR porous Si filters, one in which the total etch time was held constant and the number of cycles varied [Fig. 4], and the other in which the number of sinusoid cycles was held constant and the total etch time varied [Fig. 4]. The two calibration series share a coincident point at a sine period of p = 50 s. As expected, the etches with a constant total etch time have a similar spacing between the thin-film interference fringes, while the increasing thickness, and therefore optical thickness, of the constant-cycle etches results in a corresponding decrease in fringe spacing.

Figure 5 displays the effective optical thickness (EOT, 2n_avgL) and rugate peak position of these etches versus the period. The EOT was determined by an FFT of the thin-layer interference fringes in the visible spectrum. EOT values based on FFT of fringes in the infrared were also calculated and differed by a constant −4% from the visible values obtained at normal incidence. The filters with a constant total etch time display a slight decrease in effective optical thickness with the increasing period, in contrast to the linearly increasing EOT with period for constant-cycle, variable-etch-time filters, shown in Fig. 5. The EOT scales linearly with the period since for a constant n_avg of the layer, the thickness L is a direct function of the etch rate (in nanometers/second) multiplied by the etch time (in seconds). The rugate peak position of both the constant-time and constant-repeat etches is linear with etch period, as shown in Fig. 5. This is expected because λ₀ scales with the period p, and thus, the quantity 1/λ₀ should scale with the frequency, 1/p. Additional etches that were performed separately from the two trials above are included in Fig. 5 and show excellent agreement with these trends.

Fig. 5

(a) Effective optical thickness versus the etchwave period for porous Si optical filters. Filters fabricated with a constant total etching time (π) are compared to those etched for a constant number of sinusoid cycles (● and ■). (b) Position of the principal rugate spectral peak as a function of the frequency (1/period) for both constant-time and constant-cycle repetition calibrations.

Several issues can affect the etch rate for longer etches and, consequently, the value of EOT and the spectral peak positions. HF diffusion to the etching boundary for thick layers can lead to a decrease in the layer growth rate with depth, and a reduction of the concentration of HF as it is consumed can influence the etch rate of long-duration etches with low electrolyte volumes.^{1, 32} To address this, the volume of HF was mixed and partially replaced every 5 min during an etching procedure. Incorporation of etch stops for 1 s every cycle to allow equilibration of electrolyte concentration showed no difference in optical properties or layer thickness, though others have utilized shorter etch stops to homogenize electrolyte distribution when creating ∼300-μm-thick rugate filters with stop bands at terahertz frequencies.¹⁹ Furthermore, after a section of the filter has been electrochemically etched, it will continue to dissolve at a much lower rate while in contact with HF, leading to a high- to low-porosity gradient from the top to bottom of the etched layer. The linearity of the EOT and peak position in Fig. 5 with increasingly thicker etches and longer etch times (increasing periods for constant cycles) indicate that these issues were not significant for the samples under investigation here. The gravimetric porosity was determined for all etched layers as 74%, with no more than a ±1% variation across all samples, attributable to error in the weighing of the samples. The porosity exhibited no trend with changes in period, indicating uniformity of the etch rate with increasing etch time of the samples. It is also worth noting the decrease in the width of the rugate peaks in the FTIR spectra with increasing period. This is an expected result of changing the reflectance band position because the width of the spectral band Δλ centered at λ₀ can be expressed as^{12, 34}

The SEM thickness and effective optical thickness (2n_avgL) of a filter specimen can be used to determine the average refractive index n_avg of the porous filter For the single-peak CO₂ sensor example with a thickness of 70.7 μm, n_avg = 1.51. The refractive index of the silicon pillars in the porous material, n_Si, was then determined as 3.67 using the two-component Bruggeman effective medium approximation,³³ using a value of EOT determined from the optical interference spectrum between 850 and 1000 nm. This is a close match to the literature value of n = 3.6 at 900 nm.³⁵ This agreement indicates that the optical properties of the filters tuned to MWIR wavelengths are consistent with expected porous silicon properties.

3.4.

Demonstration of Gas Sensing with a Single-Peak Rugate

A rugate filter tuned to the ν(CO₂) band is shown in Fig. 6. The CO₂ vibrational bands between 2260 and 2390 cm⁻¹ are easily observed in a reference sample of the gas taken without the porous Si filter by using silver mirrors at all beam deflection locations. The slight sawtoothing visible around 2350 cm⁻¹ is due to incompletely resolved Q and R absorption branches (FTIR resolution was 2 cm⁻¹). The absorptions at higher wavenumbers are the result of combination vibrational modes, with a doublet at 2.7 μm and higher members of the same sequence at 2.0 μm.^{6, 7} The signals observed from 1400 to 1800 cm⁻¹ is due to a small amount of residual water vapor in the FTIR chamber.

Fig. 6

Reflectance-mode FTIR spectra demonstrating a porous Si rugate filter containing an in-band and an out-of-band peak for detection of CO₂. The rugate was etched with a single-frequency sinusoidal current-time waveform with a period p = 43.7 s. (a) Gas chamber purged with CO₂, with silver mirrors mounted in all four beam deflection locations (see Fig. 1). (b) Gas cell purged with N₂, with porous Si filter mounted at the deflection position indicated in Fig. 1. The sample was prepared such that one of the stop-band resonances appears at ∼2300 cm⁻¹, coinciding with the C–O stretching band of CO₂. The other peak (at ∼4600 cm⁻¹) is an overtone band. (c) Gas cell purged with CO₂, with porous Si at the beam deflection position indicated in Fig. 1.

The rugate filter displayed in Fig. 6 was constructed with a current-time sinusoid waveform with a period of 43.7 s etched for 45 repetitions, designed to match the 2350 cm⁻¹ principal absorption band. The resulting filter exhibited a cross-sectional thickness of 70.7 μm. On introduction of CO₂ to the gas cell, the principal rugate band was obscured by the absorbing molecules, decreasing the peak area, while the higher order harmonic was unchanged. The ratio of the areas or of the intensities of the principal peak to the harmonic overtone peak can thus be used as a referenced sensor for the presence of CO₂.

3.5.

Gas Sensing with a Composite Rugate

In the single-peak rugate described earlier, a harmonic band was utilized as a reference channel for the principal rugate band at 2350 cm⁻¹ that overlaps the CO₂ absorptions. The location of the harmonic band is spectrally distant from the principal peak and its location depends on the principal peak location. To introduce a tunable reference peak that is spectrally closer to the principal band, a composite, infrared rugate was fabricated consisting of a single layer combining two sinusoidal current-time frequencies into the current-time etch wave, as pictured in Fig. 7. Filters of each single frequency were fabricated for reference [Fig. 7], with the composite filter comprised of p = 43.7 s and p = 51 s periods that resulted in rugate bands at 2350 and 2000 cm⁻¹ respectively, with a total layer thickness of 72.5 μm determined by SEM. As shown in Fig. 7, the presence of CO₂ in the gas cell greatly reduced the area of the peak at 2350 cm⁻¹, while not affecting the reference channel at 2000 cm⁻¹. Figure 7 also demonstrates sensing of CO₂ at lower concentrations. A spectrum reflected off the filter was taken for a 50/50 volumetric mixture of CO₂ and N₂ in the gas cell, as well as ambient room air. The reflectance scan of the latter exhibits a slight reduction in the 2350 cm⁻¹ peak area and shows evidence of water vapor outside the rugate bands.

Fig. 7

Reflectance-mode FTIR detection of CO₂ using a multi-frequency rugate optical filter. (a) Single-frequency components with p = 43.7 s (middle) and p = 51 s (bottom) compared to the composite filter (top). (b) Spectra of the composite filter with varying levels of CO₂ in the gas sample cell: fully purged with CO₂ (top), 50% CO₂/50% N₂ (middle), and an ambient level of CO₂ from room air (bottom).

3.6.

Matching P=O Bond Stretching Modes

To demonstrate the ability to tune rugate peaks to the edge of the long-wave infrared region, a filter was constructed to match a typical P=O stretching vibration at 1250 cm⁻¹. This transition is present in the G-series chemical nerve agents sarin, soman, tabun, and VX.^{9, 10} The filter shown in Fig. 8 was etched with a sinusoid current-time period of p = 82.5 s, resulting in a 123-μm-thick layer as determined by SEM. Several overtone bands are clearly present.

Fig. 8

Reflectance-mode FTIR of an optical filter with a sine current-time etching waveform period of p = 82.5 s mounted at one of the beam diversion positions. The principal rugate peak at 1250 cm⁻¹ was designed to match the P=O bond stretch of G-series chemical nerve agents.