X-ray reflectivity investigation of multilayer macroporous silicon structures

In this work, the X-ray reflectivity was used to study the porosity of multilayer macroporous silicon samples obtained under various conditions. The porosity calculation is based on a change in the position of the critical angle of total external reflection resulting from a decrease in the density of the porous silicon layer. Our findings show that the absence of photoluminescence in the samples is due to a porosity of about 30 % in the surface layer. The morphological features were characterized by scanning electron and atomic force microscopy.


Introduction
Porous silicon (por-Si) is one of the promising materials for nanophotonic devices [1]. Unlike ordinary crystalline silicon (c-Si), por-Si exhibits intense photoluminescence (PL) in the visible range, as well as a large specific surface area. However, the morphology and optical properties of por-Si can vary significantly depending on the preparation technique. For example, the porosity of por-Si synthesized by top-down electrochemical etching changes from the surface to the bulk of the structure. Since PL is a surface phenomenon, with an excitation depth of about 10-30 nm for por-Si [2], it is more correct to use the surface analysis method to establish relationships between porosity and photoluminescence characteristics. It was found in the work [3] that the por-Si with a porosity of at least 50 % exhibits PL properties.
Common porosity measurement techniques such as gravimetric method, gas and liquid porosimetry determine the average porosity of a sample and are, therefore, significantly less accurate. In contrast to the above techniques, X-ray reflectivity (XRR) makes it possible to measure the density and hence the porosity of a surface layer about 10 nm thick [4]. In this paper, we discuss the morphological features, a method for determining surface porosity, and PL properties of multilayer macroporous silicon prepared under different conditions. XRR has been successfully used as a convenient non-destructive tool for measuring the porosity of the surface layer of por-Si.

Theory
The complex refractive index for the X-ray radiation can be written as [5]  Here, δ and β are the dispersion and absorption components, respectively, while r e is the classical electron radius, and λ is the wavelength of X-ray radiation. The electron density ρ e and mass density ρ are related by the expression where f denote the atomic scattering factor, f and f are the dispersion and absorption corrections, respectively, n a is the concentration of atoms, Z is the atomic number of the chemical element, N a is the Avogadro constant, and A is the atomic mass.
If we insert ρ into equation (1), we then obtain an expression for the real and imaginary parts of the refractive index In the small-angle approximation and far away from absorption edges [6], the critical angle of total external reflection can be determined according to Snell's law: Therefore, knowing the critical angles of por-Si (θ c−P S ) and silicon substrate (θ c−Si ) allows us to estimate the surface porosity from the relation [7]

Experimental methods
Multilayer macroporous silicon structures were formed on the surface of phosphorus-doped crystalline silicon c-Si(100) substrates. The one-and two-stage electrochemical etching was carried out in a solution of hydrofluoric acid and dimethylformamide with the addition of hydrogen peroxide and sulfuric acid. The anodizing current density was changed stepwise during the two-stage etching process [cf. Table 1]. The morphology and structure of the specimens were examined by scanning electron (SEM) and atomic force microscopy (AFM) using a JEOL JSM-6380 LV and NT-MDT SOLVER P47-PRO instruments, respectively. A ARL X'TRA diffractometer with a CuK α radiation, Bragg-Brentano geometry, and three resolution-defining slits was employed for scanning the XRR profiles. The PL spectra were recorded with an Ocean Optics USB4000-VIS-NIR fiber optic spectrometer; a laser diode with a radiation wavelength of 405 nm was used [8]. Table 1. Por-Si sample production conditions (etching mode, anodizing current density J, time t), thickness of the porous layer l, average Si particle size d, and surface roughness σ obtained from SEM and AFM data; porosity of the surface layer P was obtained by XRR measurements.

Results and discussion
AFM topographic images and histograms of the silicon particle size distribution of por-Si samples are shown in figure 1. The NOVA software was used for image analysis. Both samples have a porous surface and the same roughness values. However, the sample 1 obtained in a one-stage etching mode has a slightly larger average Si particle size [cf. Table 1]. In figure 2 we have gathered the cross-section SEM images of the macroporous Si samples. The SEM data show  The measured XRR data for the por-Si samples and c-Si substrate are summarized graphically in figure 3. The mesoporous Si XRR profile is also shown for comparison [9]. For incident angles θ ≤ θ c total external reflection occurs and all incoming X-rays are reflected from the surface. The intensity of the X-ray reflectivity curves drops dramatically after passing the critical angle θ > θ c . For reference, the XRR profile of a c-Si substrate was investigated. The critical angle of the c-Si substrate at which the reflected intensity is reduced by half [10] is 0.223 • and is close to the theoretical value (θ c−Si ≈ 0.22 • for λ = 1.54Å) [7]. The porosity of the macroporous silicon samples is determined by the equation (5) [cf. Table 1].
No photoluminescence was observed from the macroporous Si samples with P of less than 29 % in contrast to mesoporous Si (P=79 %). The results are in good agreement with the literature [2,3,8], according to which only por-Si with P above 50 % exhibits photoluminescent properties.

Conclusion
In this work we have studied the multilayer macroporous silicon structures prepared by an electrochemical etching method. The surface porosity of por-Si samples was determined using XRR measurements. It was demonstrated that the macroporous Si samples with P of less than 30 % do not exhibit photoluminescence. These results showed that XRR can be successfully used as a non-destructive method for investigating the porosity of the surface layer of nanophotonics devices based on por-Si.