Porous single crystalline 4H silicon carbide rugate mirrors

The electrochemical etching of semiconductors is an established method in research and industry for the realization of nanowires,¹ for sacrificial layers in surface micromachining,² or for the fabrication of optical devices.^3,4 Most of the research has been devoted to the preparation of porous silicon (pSi), either by electrochemical etching in hydrofluoric acid solutions⁵ or by metal assisted chemical etching.⁶ It could be shown that optical devices such as Bragg³ or rugate⁷ mirrors can be fabricated with those techniques. In latter mirror type, a periodic modulation of the refractive index is realized by a periodically varying degree of porosity, leading to a selective reflection of light. Bragg mirrors contain sub-layers with a fixed refractive index, while rugate filters feature a continuous refractive index profile. Such devices can be used in sensors which rely on a shift of the reflection characteristics of the mirror when the pores are filled with an analyte.⁸ However, due to its high chemical reactivity, porous silicon has drawbacks when it comes to application scenarios in harsh environments,⁹ alkaline electrolyte solutions,² or high temperatures.¹⁰ To overcome this drawback, pSi has to be covered with a dense protection layer.¹¹ 

An alternative route to obtain high temperature stable and chemically inert optical porous devices is photoelectrochemical etching (PECE) of silicon carbide (SiC). This has not been established as a reliable approach because of fabrication issues such as the presence of a skin layer on top of the porous structure or an inhomogeneous pattern of the pores.¹² Recently it was shown that a porous layer generated with metal assisted photochemical etching (MAPCE) provides initiation sites for PECE, thus avoiding skin and cap layer formation.¹³ Furthermore, the investigations preceding this study showed that constant voltage conditions lead to a constant degree of porosity, independent of the current density.¹⁴ In this study, these findings are utilized for the preparation of porous 4H silicon carbide (pSiC)-based rugate mirrors, which has not been reported so far in the literature.

For the experiments, a square-shaped (2.5 × 2.5 cm) n-type 4H–SiC sample from CREE was used, having a bulk resistivity of 0.02 Ω cm (nitrogen doping N_D-N_A ∼ 7 × 10¹⁸ cm⁻³¹⁵). First, MAPCE was performed to provide initiation sites for PECE. Therefore the sample was first cleaned by soaking consecutively in acetone and ethanol for 5 min. Next, inverse sputter etching was done for 240 s at a plasma power of 200 W, utilizing a LS730S Von Ardenne sputter machine. Afterwards 300 nm of platinum (Pt) were sputter deposited at the corners of the sample having a total area of approximately 1 cm². Then the sample was annealed in a Nabertherm L9/11/SKM oven for 5 min at 1100 °C under argon flow with a prior 30 min temperature ramp starting at 800 °C to decrease the contact resistance at the Pt/SiC interface.¹⁶ Finally the sample was immersed in 10 ml of a solution containing 0.15 mol/l Na₂S₂O₈ and 1.31 mol/l HF and irradiated from a distance of approximately 1 cm with a custom built UV source having its peak wavelength at 254 nm. This etching procedure lasted for 30 min and was repeated 4 times with fresh etching solution, leading to an approximately 1 $μ$m thick porous layer on top of the sample. The theoretical details of this MAPCE process can be found elsewhere.¹⁶ 

Finally PECE was performed in a porous silicon etching chamber from AMMT GmbH. The active volume of the etching solution (0.04M Na₂S₂O₈ in 1.31 mol/l HF) was approximately 150 ml, while UV light irradiation was done with a 250 W ES280LL mercury arc lamp at full spectrum. During PECE, a circular area of 3.14 cm² in the middle of the sample was porosified, such that no Pt was in the area of the mirror elements.

During PECE, a 12 step sinusoidal voltage profile was applied with a CPX400DP Dual 420 W power supply from Aim-TTi because in pre-investigations it was found that the applied voltage determines the resulting porosity independent of the current density. However, a decreasing current density during experiments caused a drop in the etch rate. Therefore, etching was performed in a charge controlled mode. This means that a defined amount of charge has to be transferred during each constant voltage step, counterbalancing the decreasing etching rate. To obtain similar etching depths during each step, the amount of charge per step is weighted such that more charge is transferred at a higher voltage because under these conditions the resulting porosity is higher but the etching rate is decreased. The applied voltage profile can be found in Table I. During PECE, this profile was executed 150 times after an initial phase of 11.5 V which lasted for 3 s. Finally, two 60 V pulses, each lasting 6 s, were applied to separate the porous layer from the bulk sample. This way the bulk sample can be re-used for mirror preparation by repeating the previous sequence of MAPCE and PECE steps.

All etching experiments were performed on the Si-face of the 4H–SiC sample. To obtain cross-sectional micrographs, the separated porous thin film was cracked and investigated with a Hitachi SU8030 scanning electron microscope (SEM) using acceleration voltages between 1 kV and 5 kV. Reflectance spectra were recorded with a Filmetrics F20 layer thickness measurement device. Reflectance measurements were performed on the side at which separation from the bulk took place.

First, the resulting pore morphology of the mirror was investigated by analyzing cross-sectional SEM micrographs. Figure 1 shows such a SEM micrograph with the corresponding black and white image which was obtained with adaptive Gaussian image thresholding.¹³ The degree of porosity varies between low and high values, whereas the pore morphology varies between low and high porosity dendritic according to the classification in the literature.¹⁷ The numerical value of the degree of porosity profile could be estimated from the black and white images as is shown in Fig. 2(a). Additionally the distribution of the pore cross-sectional area contributing to the total degree of porosity is shown in Fig. 2(b). Pores with a cross-sectional area of approximately 350 nm² appear most often in this distribution. The porosity profile, in turn, allowed the calculation of the refractive index profile n_eff according to the following equation, which relies on the Bruggeman effective medium theory:¹⁸ 

The refractive index of hexagonal SiC n_SiC is 2.62 at a wavelength of 710 nm,¹⁹ while n_Pore stands for the refractive index of the pores, which is 1. The porosity is given by p and d is the dimensionality of the system, which is set to 3.

A section of the obtained refractive index profile is shown in Fig. 2(c). The refractive index varies periodically, and the fast Fourier transform of the whole refractive index profile shows two peaks at 5.9 $μ$m⁻¹ and 11.8 $μ$m⁻¹ [see Fig. 2(d)]. This allows the prediction of the rejection wavelengths in the reflectance of the mirror according to the following equation:

Here 〈n〉 is the average refractive index of the mirror and z is the length of a period.²⁰ According to Eq. 2 and the calculated data from the experiment (z₁ = 0.0847; z₂ = 0.169; 〈n〉 = 2.109), one expects two peaks in the reflectance spectrum at rejection wavelengths of 357 and 713 nm. This was indeed found in reflectance measurements as is illustrated in Fig. 3(a). Three measurements of the prepared mirror are shown which exhibit peaks at 375–385 nm and 710–750 nm which correspond to the prediction from the refractive index profile.

A more rigorous calculation of the reflectance spectrum has also been performed with the program OpenFilters neglecting front and back side reflections.²¹ The result is illustrated in Fig. 3(b), demonstrating that the rejection wavelengths are located at approximately 360 and 720 nm. Also the physical appearance of the prepared mirror is in accordance with the measurements as can be seen in Fig. 3(c). It appears in green because in transmission one can see the complementary colors of the reflectance spectrum. This indicates that such mirrors can also be used in the transmission mode.

Finally, the possibility to re-use the dense 4H SiC sample for subsequent mirror fabrication is demonstrated. Therefore, the same etching procedure (i.e., MAPCE and PECE) was performed as used for the realization of the first rugate mirror element. Only the applied voltage profile was modified, such that the transferred charge during the porosification sequence was increased (see Table II). This was done to show additionally whether the peak positions in the reflectance spectrum can be shifted to higher values.

The resulting reflectance spectra are illustrated in Fig. 4(a). As expected, the two reflectance peaks shifted to larger values of 440–460 nm and 810–920 nm compared to those illustrated in Fig. 3(a). In Fig. 4(b), the calculated reflectance spectrum is shown, proving on a theoretical basis, the increase of the rejection wavelengths. Finally, it is worth mentioning that the physical appearance of the mirror changes when applying the modified parameters during PECE. Instead of green, it appears now in yellow, being the complementary color of the minor peak located at 440–460 nm. Besides these observations, also the total mirror thickness increased from about 28 to 35 $μ$m. In both cases, the separation from the bulk substrate succeeded at the end of the etching sequence, so the etching depth equals the final mirror thickness.

Porous 4H–SiC rugate mirrors were fabricated for the first time with a combination of metal assisted photochemical etching (MAPCE) and photoelectrochemical etching (PECE). It turned out that varying the voltage as a function of transferred charge is suitable for obtaining a sinusoidal porosity profile. The refractive index profile could be estimated with image processing methods, thus enabling to estimate the rejection wavelengths of each mirror. This demonstrates that image processing can be most beneficially applied when designing even more complex reflection spectra. Furthermore the presented method allows us to control the reflectance spectrum and the re-use of the 4H–SiC substrates, which is of economic interest.

In conclusion, the presented results show that pSiC is a possible alternative to pSi for the fabrication of optical filters, especially when targeting application scenarios in harsh environments.

This project has been supported by the COMET K1 centre ASSIC Austrian Smart Systems Integration Research Center. The COMET—Competence Centers for Excellent Technologies—Programme is supported by BMVIT, BMWFW, and the federal provinces of Carinthia and Styria. The authors acknowledge the TU Wien University Library for financial support through its Open Access Funding Program.