Electromagnetic waves in non-absorbing medium

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Total reflectance and transmittance measurements

PerkinElmer UV/Vis/NIR spectrophotometer Lambda 950 with a 150 mm integrating sphere has been used to measure the sum of total reflectance and transmittance of the pyramidal textured wafers to assess the impact of the surface texture on the light-trapping properties. The sum of the total specular and diffuse reflectance and transmittance of the sample corresponding to (R + T = 1 − A), where A is the absorptance, has been measured with the sample inside the integrating sphere in the spectral range from 250 to 1100 nm with an increment of 5 nm. All six samples with different surface treatments (see Fig. 2.2) were measured at the normal angle of incidence (AOI) with respect to the plane of the wafer. Second, both types of samples with no additional surface post-treatment (A1 and B1) were also measured at oblique angles of incidence reaching values from 8◦ to 60◦.

Standard and Mueller matrix ellipsometry

The advantage of using ellipsometric techniques such as standard spectroscopic ellipsometry or Mueller matrix polarimetry is, that in contrast with the spectroscopy presented above in Section 3.1, the ellipsometric techniques measure not only the change of amplitude but also the phase shift of polarized light after its interaction with a sample. This allow us to obtain more information about the studied sample. Following subsections describe measurement set-ups for different types of ellipsometric techniques used for characterization of samples in this thesis. More details on the principles of ellipsometric measurements and the theory behind data analysis can be find in Section 4.3 of Chapter 4.

Standard spectroscopic ellipsometry

Ex-situ scanning spectroscopic phase modulated ellipsometer measurements (Uvisel 2, Horiba Scientific) of reference samples have been carried out to determine optical functions of used materials. The Uvisel 2 with the 150 W Xenon light source was used to measure reference samples of of a-Si:H, a-SiC:H, (p)a- Si:H, (p++)a-Si:H, ITO, Sn and ZnO:Al thin films on Corning glass substrates. The measurements have been performed in a wide spectral range of 230-2000 nm (0.6-5.4 eV) at the angle of incidence of 70◦. Spectroscopic ellipsometry on pyramidal textures Reduced reflectivity and high scattering of the pyramidal textured surface require an increased light source intensity and specific measurement configurations for ellipsometric signal with a good signal to noise ratio [8]. Scanning spectroscopic phase modulated ellipsometer UVISEL 2 (Horiba Scientific) with a 150 W Xenon light source has been used to measure spectroscopic ellipsometry data of samples with pyramidal texture. This ellipsometer is equipped with a double monochromator system for the ultraviolet-visible (UV-VIS) range from 190 nm to 880 nm and twin photomultiplier tube detectors for the higher sensitivity and dynamic range. It has a near-infrared (NIR) extension, covering the spectral range up to 2100 nm, consisting of monochromator for NIR range (880-2100 nm) and InGaAs detector. This ellipsometer allows variable angle spectroscopic ellipsometry measurements in the range from 35◦ to 90◦.
The lateral measurement geometry, which is based on aligning the pyramidal facets perpendicular to the plane of incidence, was used for measurements as described in Ref. [9]. An inclination stage has been used to align a sample to the required position in order to obtain specular reflection from the facets (for illustration see Fig. 3.1). First, the angle of incidence, set by a goniometer, was verified by a measurement of the reference flat wafer with a 22.1 nm layer of thermal oxide. Then, the textured sample was mounted on the inclination stage so that one straight edge of the quarter-wafer representing the [1¯10] direction was parallel to the plane of incidence. The computer controlled XYZ stage was used to adjust the spatial position of the sample. Then, we inclined the sample using the inclination stage to set the (1¯1 ¯1 ) facets of the pyramids to be in horizontal sample plane. The ideal inclination angle of 54.74◦ (for ideal pyramids) corresponds to the angle between a facet and a base of a pyramid defined by the geometry of anisotropic wet-etching. The inclination angle of the stage was set to 55◦ and then tuned manually for particular sample geometry to maximize the brightness of the spot displayed by the vision system providing a real-time color image of the sample and exact measurement spot using the ellipsometer head.

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In-situ spectroscopic Mueller matrix ellipsometry

We have used a Mueller matrix polarimeter (MM-16, Horiba Scientific) for a fast, non-destructive, large spot characterization of random silicon nanowire arrays during their growth. The MM-16 polarimeter has a liquid crystal based polarization state generator and analyzer allowing for measurements of all 15 elements of normalized Mueller matrices in the spectral range of 450 – 850 nm. Heads of MM-16 are fixed to the PECVD reactor windows (as shown in Fig. 3.2) to enable in-situ measurements during the deposition at the fixed angle of incidence of 71.2◦. In-situ ellipsometric data has been measured every 1 min during sample fabrication starting from Sn droplets formation by H2 plasma treatment and continuing during SiNW growth.

Angle-resolved Mueller matrix ellipsometry

We have used angle-resolved Mueller matrix polarimeter (AR-MMP) with microscope objective of high numerical aperture (NA = 0.95) to measure complete Mueller matrices over the range of polar angles # (0-60◦) and azimuthal angles (0-360◦). The polarimeter enables measurements of all elements of Mueller matrix in real and Fourier space at the same spot on the sample. A patented calibration [53] of this device is based on the single value decomposition [54]. The spot size diameter can be adjusted from a few micrometers up to 50 μm using an iris aperture. A halogen lamp was used as the light source. For more information on the measurement setup see Ref. 55. We have used a fine pinhole aperture to select only the near normal angle of incidence from the objective back focal plane.

Table of contents :

Acknowledgements
Abstracts
Contents
List of symbols
1 Introduction 
1.1 Photovoltaic applications.
1.2 State of the art
1.3 Objective of the work
1.4 Organization of the thesis
2 Sample preparation
2.1 Silicon heterojunction solar cells.
2.1.1 Description of textured wafers
2.2 Radial junction solar cells
2.2.1 Silicon nanowires grown for radial junction solar cells
3 Characterization methods 
3.1 Total reflectance and transmittance measurements
3.2 Standard and Mueller matrix ellipsometry.
3.2.1 Standard spectroscopic ellipsometry
3.2.2 In-situ spectroscopic Mueller matrix ellipsometry
3.2.3 Angle-resolved Mueller matrix ellipsometry
4 Theoretical background 
4.1 Electromagnetic theory of light
4.1.1 Maxwell equations in general medium
4.1.2 Classification of material media
4.1.3 Electromagnetic waves in non-absorbing medium
4.1.4 Electromagnetic waves in absorbing medium
4.2 Light propagation in thin film systems
4.2.1 Yeh’s matrix formalism
4.2.2 Optical intensity and power
4.2.3 Reflection and transmission of light
4.3 Principles of ellipsometric techniques
4.3.1 Principles of spectroscopic ellipsometry
4.3.2 Principles of Mueller matrix polarimetry
4.3.3 Data analysis
5 Results for pyramidal textured samples 
5.1 Reflectance of pyramidal textured surfaces
5.2 Analysis of angles of pyramids
5.2.1 Measurement of the angles of pyramids
5.2.2 Origin of different pyramidal angles
5.3 Analysis of thin films on pyramids
5.3.1 Consequences of vertex angle variation
5.3.2 Model of spectroscopic ellipsometry data.
5.3.3 Optimization of multi-layer system
5.3.4 Silicon heterojunction solar cells
5.4 Chapter key results
6 Results for silicon nanowires 
6.1 Characterization of used materials
6.2 Substrate characterization before nanowire growth.
6.3 In-situ characterization of silicon nanowire growth.
6.4 Ex-situ characterization after nanowire growth
6.5 Chapter key results
Conclusions and perspectives
Conclusions
Perspectives
A Optical functions of materials 
Intrinsic hydrogenated amorphous silicon (i)a-Si:H
Intrinsic hydrogenated amorphous silicon carbide (i)a-SiC:H.
P-type hydrogenated amorphous silicon (p)a-Si:H and (p++)a-Si:H
Indium tin oxide ITO.
List of figures
List of tables
List of publications
References

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