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Optical Characterization of Porous Silicon Multilayers

  • Ugur Cem Hasar
  • Ibrahim Yucel Ozbek
  • Tehvit Karacali
Living reference work entry

Abstract

Uncontrolled fabrication errors for multilayer porous silicon structures could in some circumstances significantly and unexpectedly change their optical properties (reflectivity, refractive index, etc.). Therefore, optical characterization of these structures gains prominent importance before using these structures for various applications such as optoelectronics and sensing. It is the aim of this short review to discuss the importance of optical characterization of multilayer porous silicon structures, by way of some numerical modeling and experimental results. We will thereby illustrate some important aspects about how the optical performance of these structures can be increased by following some simple precautions in their fabrication. It is also our objective in this review to bring some of the recent studies and trends in the subject of optical characterization to the attention of readers.

Keywords

Measurement Multilayered porous silicon Numerical analysis Optical characterization 

Introduction

Porous silicon structures have promising applications in photonics (Canham 1997; Escorcia-Garcia et al. 2009), luminescence (Cullis and Canham 1991), and sensors (Lorenzo et al. 2005) thanks to their high surface to volume ratio, integration with surface areas across a chip surface, and highly variable surface chemistry.

In addition to their structural, thermal, mechanical, and optical properties (see the handbook chapters “➔Microscopy of Porous Silicon,” “➔Thermal Properties of Porous Silicon,” “➔Mechanical Properties of Porous Silicon,” and “➔Refractive Index of Porous Silicon”), characterization of porous structures also plays a key role to fully investigate the behavior and response of porous silicon structures (for more details, see the handbook chapters “➔Characterization of Porous Silicon by Calorimetry,” “➔Magnetic Characterization Methods for Porous Silicon,” “➔Chemical Characterization of Porous Silicon,” and “➔Characterization of Porous Silicon by Infrared Spectroscopy”).

Porous silicon structures with miscellaneous properties (Rugate-filter, Fabry-Perot, or microcavity structure; multilayer or freestanding form) can be created by a simple and easy electrochemical anodic etching process. This process can in addition provide a broad refractive index contrast, a desirable feature in sensing applications. For more details, please refer to the book chapter “➔Porous Silicon Multilayers and Superlattices.” However, some uncontrolled fabrication errors, to be discussed in the following sections, alter the optical properties (refractive index, extinction coefficient, wavelength shift, reflectivity, and transmittivity) of porous structures, changing in turn their sensing performance. Therefore, optical porous silicon sensors have to be characterized to investigate their non-ideal characteristics before sensing applications such as organic vapor detection (Liu et al. 2009; Cho et al. 2013; Karacali et al. 2013; Hasar et al. 2015a) and inorganic gas vapor detection (Yan et al. 2014).

Optical characterization of porous silicon multilayer structures can be analyzed by different measurements such as photoluminescence, ellipsometry, and reflectometry. The photoluminescence measurements record spontaneous emission of light from porous silicon structures under optical excitation (Canham 1990; Pelant and Valenta 2012). Ellipsometry measurement is an optical characterization technique utilizing measurement of the polarization transformation that occurs after the reflection (or the transmission) of a polarized beam (Azzam and Bashara 1989; Tompkins and McGahan 1999; Pérez 2007). On the other hand, reflectometry or interferometry measurement , as its name specifies, is based on the response of interference phenomenon inside a material (Tompkins and McGahan 1999).

In the following short review, we first look at the nature of fabrication errors in preparation of multilayer porous silicon structures. Next, we present the basic theory for modeling the optical characterization of porous silicon structures and, then, demonstrate a typical measurement setup which could be used for optical characterization. Finally, we recapitulate some of the important findings of this review.

Modeling for Optical Characterization

In the electrochemical etching technique , generally controllable current densities are applied for some specific time over a p-type (or n-type) uniformly doped bulk silicon sample located within an etching cell (or tank) to fabricate multilayer porous silicon structures with desirable optical properties (Pavesi 1997; Agarwal et al. 2009; Ghulinyan et al. 2003a; Sailor 2012). Related book chapter is “➔Porous Silicon Multilayers and Superlattices.” Enlargement of current passage across first created layers due to long stay time of the sample in the electrolyte (Pavesi 1997; Ghulinyan et al. 2003a) and presence of some surface irregularities and internal impurities [doping inhomogeneities (Ghulinyan et al. 2003a)] can induce as a whole different optical properties in the axial dimension of multilayer porous silicon structures. Additionally, nonuniform surface current densities, natural drifts in the growth direction (Ghulinyan et al. 2003a), and dopant impurities can also result in different optical properties in the transverse dimension of these structures. Furthermore, higher variation of refractive index (a desirable property for increasing selectivity of sensors), which can be attained by low resistive substrates, large current variation, and a proper electrolyte concentration, is generally accompanied by an increased macroscopic roughness due to striations (Setzu et al. 2000). Therefore, effects of these fabrication errors on optical properties of porous multilayer structures need to be investigated for the analysis of their optical performance and sensing capability by performing a thorough optical characterization.

For analyzing the optical response and characterization of multilayer porous silicon structures, macroscopic electromagnetic properties (e.g., refractive index and extinction coefficient) are used for describing electromagnetic responses (reflectivity and transmittivity) of these microscopically inhomogeneous but homogenized structures. These properties will be effective ones if the value of the operating wavelength is much higher than the diameter of the pores in each fabricated layer (effective medium theory) (Saarinen et al. 2008; Suarez et al. 2011). In this circumstance, different effective medium approximations can be used such as Maxwell-Garnett, Bruggeman, or their mixture (Jylha and Sihvola 2007). Such approximations relate the optical properties of each constituent (e.g., pore and bulk silicon) of the composite porous silicon layer to effective optical properties.

Most of the time, global optical responses (wavelength shift, reflectivity, and transmittivity) at front and back surfaces of a whole multilayer porous structure are analyzed for their modeling and optical characterization in contrast to full but not-so-necessary response (responses at front and back surfaces as well as interior region) of these structures. In such a case, either transfer matrix method – TMM (Lorenzo et al. 2005; Pavesi 1997; Snow et al. 1999; Ghulinyan et al. 2003a, 2003b; Torres-Costa et al. 2004; Ouyang et al. 2006; Moretti et al. 2006; Saarinen et al. 2008; Karacali et al. 2009; Charrier and Dribek 2010; Hasar et al. 2012; Palavicini and Wang 2013) – or wave cascade matrix method (Hasar et al. 2015b) could be applied for obtaining reflectivity (and transmittivity) and ellipsometry responses of a whole multilayer porous structure. Some of the more informative studies for optical characterization of porous silicon multilayer structures by reflectivity and ellipsometry measurements are given in Table 1.
Table 1

Selected example studies related to optical characterization of porous silicon multilayers by different techniques and with different objectives

1. Effects of optical loss coefficient of Si substrate on transmittivity of freestanding single and coupled microcavities were analyzed (Ghulinyan et al. 2003a)

2. Wavelength shift of Bragg mirrors was analyzed by considering the capillary condensation effect after exposure of the mirrors to organic vapors (Snow et al. 1999)

3. Effects of optical loss coefficient of Si substrate on transmittivity of freestanding single and coupled microcavities were analyzed (Ghulinyan et al. 2003a)

4. Influence of linear drifts in porosity and thickness of the layers on reflectivity and transmittivity of freestanding coupled microcavities was investigated (Ghulinyan et al. 2003b)

5. Optical constants (complex refractive index and thickness) of each layer of multilayer periodic Bragg mirrors were determined by using genetic algorithms (Torres-Costa et al. 2004)

6. Photonic band gap properties of quasi-periodic Thue-Morse and Fibonacci porous silicon multilayer structures were investigated from oblique incidence case (Moretti et al. 2006; Palavicini and Wang 2013)

7. Quantitative analysis of the effect of pore diameter on the refractive index and thus sensitivity of porous silicon optical biosensors was performed (Ouyang et al. 2006)

8. Analysis for reflectance spectrum of multilayer one-dimensional microcavity porous silicon structure for off-normal incidence (s- and p-polarizations) considering a uniaxially anisotropic dielectric tensor was carried out (Saarinen et al. 2008)

9. Effects of surface modification (formation of silicon dioxide, occurrence of volume expansion due to oxidation, and application of sensed analyte) on the effective refractive index of periodic porous silicon Bragg mirrors and microcavities for biosensing applications were examined (Charrier and Dribek 2010; Suarez et al. 2011)

10. Effects of variations in thickness, refractive index, and extinction coefficient of each individual layer on reflectivity and transmittivity of multilayer Fabry-Perot porous silicon structures were evaluated (Hasar et al. 2012; 2015b)

11. Optical response of porous silicon Bragg reflectors was measured by variable angle-of-incidence infrared spectroscopic ellipsometry technique (Zangooie et al. 2001)

The overall interference response (M h ) of a multilayer porous silicon structure with N layer by reflectometry measurements can be found by application of the TMM [for the exp(+iωt) time reference] (Born and Wolf 1999).

$$ \left[{M}_h\right]=\left[\begin{array}{cc}\hfill {m}_{11}^h\hfill & \hfill {m}_{12}^h\hfill \\ {}\hfill {m}_{21}^h\hfill & \hfill {m}_{22}^h\hfill \end{array}\right]=\prod_{k=1}^N\left[\begin{array}{cc}\hfill \cos \left({k}_0{n}_{ck}{d}_k \cos {\theta}_k\right)\hfill & \hfill \frac{i}{p_k} \sin \left({k}_0{n}_{ck}{d}_k \cos {\theta}_k\right)\hfill \\ {}\hfill { i p}_k \sin \left({k}_0{n}_{ck}{d}_k \cos {\theta}_k\right)\hfill & \hfill \cos \left({k}_0{n}_{ck}{d}_k \cos {\theta}_k\right)\hfill \end{array}\right], $$
(1)
where h and k denote the overall structure and the dummy index; \( {m}_{11}^h \), \( {m}_{12}^h \), \( {m}_{21}^h \), and \( {m}_{22}^h \) are the entries of M h ; θ k corresponds to refraction angle; p k  = n ck  cos θ k for TE polarized wave and p k  = n ck / cos θ k for TM polarized wave; n ck  = n k  −  k and d k designate the effective refractive index and the thickness of any layer; n k and κ k mean the real and imaginary parts of the complex refractive index of any layer; and k 0 shows the free-space phase constant (or wavenumber). Then, reflectivity (R) and transmittivity (T) of the porous silicon multilayer structure (with bulk silicon substrate) for normal incidence case (θ k  = 0) can be obtained from (Hasar et al. 2012, 2015b)
$$ R={\left|\frac{\left({m}_{11}^T+{n}_{\mathrm{Si}}{m}_{12}^T\right){n}_{\mathrm{air}}-\left({m}_{21}^T+{n}_{\mathrm{Si}}{m}_{22}^T\right)}{\left({m}_{11}^T+{n}_{\mathrm{Si}}{m}_{12}^T\right){n}_{\mathrm{air}}+\left({m}_{21}^T+{n}_{\mathrm{Si}}{m}_{22}^T\right)}\right|}^2, $$
(2)
$$ T=\left|\frac{n_{\mathrm{Si}}}{n_{\mathrm{air}}}\right|\left|\frac{2{n}_{\mathrm{air}}}{\left({m}_{11}^T+{n}_{\mathrm{Si}}{m}_2^T\right){n}_{\mathrm{air}}+\left({m}_{21}^T+{n}_{\mathrm{Si}}{m}_{22}^T\right)}\right| $$
(3)
where n Si and n air correspond to the refractive indices of bulk silicon and air.

On the other hand, the ellipsometric parameters in ellipsometry measurements can be related to the reflection coefficients of the light polarized parallel and perpendicular to the plane of incidence r p and r s , respectively. The measured complex ratio ρ (modulus and phase) of the these two reflection coefficients is defined as (Azzam and Bashara 1989; Tompkins and McGahan 1999; Pérez 2007; Zangooie et al. 2001)

$$ \rho =\frac{r_p}{r_s}= \tan \left(\psi \right){e}^{i\Delta}, $$
(4)
where tan(ψ) denotes the ratio of amplitude changes and Δ is the relative difference in phase changes between r p and r s upon reflection. Similar to the ellipsometric parameters tan(ψ) and Δ, other similar parameters I S and I C in terms of ψ and Δ could be used as well (Pérez 2007). Incorporating Eq. 1, it is possible to relate the measured ρ m with its theoretical one (Zangooie et al. 2001).
As a representative example for optical characterization of multilayer porous silicon structures, Fig. 1a, b illustrate, respectively, the dependencies of wavelength shifts and reflectivity (R) of a Fabry-Perot porous silicon cavity over a percentage change in refractive index of any cavity layer [normal incidence and with silicon substrate]. This cavity is assumed to be resonating at λ 01 = 1473 nm and has a total number of 40 layers, refractive indices of 1.75 and 2.50, and thicknesses of approximately 210 nm and 147 nm for high- and low-porosity layers. The substrate thickness of the cavity is 800 μm. While the first layers are next to air-porous silicon interface, the last layers are next to the porous silicon substrate interface.
Fig. 1

Effect of percentage change in layer refractive index on (a) resonance wavelength (λ) and (b) reflectivity (R) of a lossless porous silicon Fabry-Perot cavity (40 layers and a resonance wavelength of λ 01 = 1473 nm)

It is seen from Fig. 1a that a change in refractive index of middle layers drastically affects the resonance characteristics of Fabry-Perot cavities . This is an important issue for fabrication of thick multilayer porous silicon cavities since variation of electrolyte concentration could pose a porosity gradient along the depth of the cavity as a consequence of diffusion issue (Thonissen and Berger 1997). In addition, the dependence in Fig. 1a shows that for the fabrication of Fabry-Perot cavities, low resistive p++ type substrates [assuming appropriate electrolyte solution, viscosity level, and pulsed anodic etching are used (James et al. 2009)] could be preferred to high resistive ones to increase the interface quality (decrease interface roughness) between the layers (Escorcia-Garcia et al. 2009). On the other hand, as seen from Fig. 1b that a similar change of refractive index of almost all layers (from first to last) alters the reflectivity value of Fabry-Perot cavities, demonstrating as well a caution on fabrication of Fabry-Perot cavities considering above fabrication recipes.

The dependencies in Fig. 1 are obtained for a Fabry-Perot cavity resonating at λ 01 = 1473 nm, which can be regarded as a lossless cavity due to the insignificant value of extinction coefficient of effective refractive index over the analyzed wavelength region. As a demonstration of the effect of extinction coefficient on the reflectivity and transmittivity values, we consider a low-loss Fabry-Perot cavity resonating at λ 02 = 530 nm (its number of layers is 24, refractive indices of 1.45−i0.010 and 2.01−i0.015, and thicknesses of 91.4 nm and 65.9 nm for high- and low-porosity layers) with its optical properties shown in Fig. 2. The substrate thickness of the cavity is 90 μm. It is seen from Fig. 2a, b that while reflectivity of a lossy porous silicon multilayered structure mainly depends on a change in refractive index of the first layers (due to loss character), its transmittivity changes throughout the whole structure.
Fig. 2

Effect of percentage change in layer refractive index on (a) reflectivity (R) and (b) transmittivity (T) of a low-loss porous silicon Fabry-Perot cavity (24 layers and a resonance wavelength of λ 02 = 530 nm)

In addition to the analysis of changes in refractive index of a multilayered Fabry-Perot cavity due to fabrication errors such as nonuniform surface current densities and enlargement of current passage, the effect of a change in layer thickness of multilayered Fabry-Perot cavities (arising from fabrication errors) on their optical properties is also important. Figure 3a, b demonstrate the effect of a percentage change in layer thickness on reflectivity (R) of the lossless and low-loss multilayered Fabry-Perot cavities resonating at λ 01 = 1473 nm and λ 02 = 530 nm whose optical properties are discussed above. We observe from Figs. 2a and 3a and from Figs. 1b and 3b that while effects of layer refractive index and layer thickness of the lossless multilayered cavity on its reflectivity are almost identical, those of the low-loss multilayered cavity on its reflectivity are totally different and independent. This indicates that for a multilayered cavity with substantial Si substrate loss, effect of a change in optical length should be analyzed not only by a change in layer refractive index but also by a change in layer thickness, as different from the case of a multilayered cavity with negligible loss.
Fig. 3

Effect of percentage change in layer thickness on reflectivity (R) of (a) the low-loss porous silicon Fabry-Perot cavity (24 layers and a resonance wavelength of λ02 = 530 nm) and (b) the lossless porous silicon Fabry-Perot cavity (40 layers and a resonance wavelength of λ01 = 1473 nm)

Measurement Setup for Optical Calibration of Porous Multilayer Structures

Numerical analysis for optical characterization can provide insight regarding the effect of fabrication errors of porous multilayer structures. However, for a complete optical characterization, in addition to numerical analysis, measurements of reflectivity and/or transmittivity of empty porous multilayer structures should be carried out.

Figure 4a illustrates the schematic view of a typical setup used for reflectivity measurements of multilayered porous silicon sensors. Here, a tungsten-halogen lamp from Ocean Optics R-LS operating in the 450–1700 nm wavelength range is used for light source. The spectrometer from Ocean Optics NIR512 measures reflectivity spectrum in the 900–1700 nm range with 1.7 nm optic resolution. Bifurcated optical multimode fiber (BFMF) from Ocean Optics (QBIF600-VIS-NIR) is utilized to separate incident and reflected signals. Splice bushing (SB) and MMF patch cord are both employed for carrying incident and reflected signals. The xyz stage with 1 μm resolution is applied for arranging reflectivity measurements from various positions of the surface of the multilayer porous silicon structure. More details of the setup can be found in (Hasar et al. 2012, 2015b; Karacali et al. 2013; Hasar et al. 2015b). For a more accurate setup for precise measurements including a microscope 25Х objective for focusing, the reader can also refer to (Ghulinyan et al. 2003a). Figure 4b illustrates a photo of the measurement setup used for reflectivity measurements at Advanced Sensor Technologies Laboratory at Electrical and Electronics Engineering Department in Atatürk University in Erzurum, Turkey.
Fig. 4

(a) Schematic view of a typical setup for reflectivity measurements of porous silicon multilayer structures and (b) a photo of the measurement setup used for reflectivity measurements at our Advanced Sensor Technologies Laboratory

Before starting measurements for optical characterization, the setup should be calibrated. Toward this end, firstly apertures of fiber optic cables should be properly oriented so that maximum reflection is possible. Second, reflected signal from a flat highly reflective (alumina) plate (around 99.7%), which will be used as a reference signal for reflectivity measurements, should be measured. Then, for each wavelength, reflectivity measurements over the whole band could be achieved by dividing the reflected signal from the porous structure to the signal from the plate used. If needed, the effect of dark signal (no lamp signal) could also be included into reflectivity measurements to improve the measurement accuracy.

Figure 5a, b show measured reflectivity from four points over the surface (and approximately at the center) of two fabricated Fabry-Perot cavities (lossless cavity with 40 layers and λ 01 = 1456 nm and lossy cavity with 24 layers and λ 02 = 542 nm). In the fabrication, current densities of 50 mA/cm2 (75 mA/cm2) and 6 mA/cm2 (2 mA/cm2) are supplied for 5.5 s (9.9 s) and 14.4 s (36.8 s) for the formation of high- and low-porosity layers of the lossless (lossy) cavity, respectively. Microcavity region of the lossless (lossy) cavity is created by applying the current density of 50 mA/cm2 (75 mA/cm2) during 11.0 s (19.8 s). Electrochemical pulsed anodic etching in the HF-ethanol solution [HF (40%) and ethanol (95%) by a 1:2 ratio] is used in the fabrication process. Substrate thickness of the lossless (lossy) cavity is around 800 μm (90 μm) measured by a high-precision nanometer profile-measuring instrument AEP-NanoMap 500LS (3D contact profilometer) by AEP technology (Hasar et al. 2015b). It has a 0.1 nm fine range and 0.01 μm coarse range resolution in vertical direction and 0.1 μm resolution in horizontal directions.
Fig. 5

Measured reflectivity (R) from four points (separated from one another approximately 25 μm) over the surface and approximately at the center of fabricated (a) lossless and (b) lossy Fabry-Perot cavities

It is seen from Fig. 5 that the whole spectrum of reflectivity of both cavities changes from point to point. This is because reflectivity is associated with changes in optical (refractive index) and physical (thickness) properties of any layer (or layers). Besides, variation of resonance wavelength indicates that either effective refractive index and/or thickness of layers (or a layer) near microcavity region changes (Hasar et al. 2015b). Resonance wavelength of the lossless cavity changes more than that of the lossy cavity for the same amount of surface point variation (25 μm), necessitating more careful fabrication of lossless multilayer porous silicon structures than their lossy counterparts.

Conclusion

This review has collated information about the current trends and stage of optical characterization of multilayer porous silicon structures. It is noted that fabrication errors such as nonuniform surface current densities and doping inhomogeneities, along with the effect of surface modification, could significantly alter the optical properties, via a change in refractive index and thickness, of especially multilayer porous silicon structures, if proper attention is not exercised in the fabrication process. Thus, considering the ever-increasing demand for application of porous silicon sensors in biology, medicine, and food and beverage control quality, optical characterization of these sensors plays a key role and thus an indispensable part in detection and identification of unknown agents (organic or inorganic gas vapor, biological or chemical molecule, etc.).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ugur Cem Hasar
    • 1
  • Ibrahim Yucel Ozbek
    • 2
  • Tehvit Karacali
    • 2
  1. 1.Department of Electrical and Electronics Engineering, Gaziantep UniversityGaziantepTurkey
  2. 2.Department of Electrical and Electronics EngineeringAtatürk UniversityErzurumTurkey

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