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We identified for the first time a specific case in which convection of heat is critical in the accurate modeling of PDS experiments. Specifically, when a sample-substrate system has very low thermal conductivity and a photothermal fluid contains a small fraction of highly thermally conducting nanoparticles, convection becomes important to analyze PDS data. We developed two different models for conduction-driven and convection- driven PDS experiments and we experimentally quantified the contribution of convective heat transfer in the case of a photothermal fluid in which highly thermally conducting nanoparticles are dispersed. For our quantitative measurements, we used carbon tetrachloride (CCl4) with varying fractions of CNTs dispersed in it as the photothermal

fluid and the effect of such dispersion on the amplitude and phase of PDS signal during the spectroscopic PDS measurements of a PEDOT:PSS thin film on a thermally insulating substrate. We find that the amplitude of angle of deflection increases with increasing concentrations of CNTs in CCl4 provided that the suspension retains a

sufficiently high transparency and the change in the fluid viscosity is minimal. Our results support the experimental evidence reported in the literature [28] abut the heat transfer processes between a nanofluid and a solid surface in the case of natural convection. When nanoparticles concentration is above a certain value, the Prandtl number of nanofluid becomes significantly low (~10-3) and buoyancy equilibration by inertia determines the heat transfer coefficient that only increases very slowly with the CNTs concentration. When heat transfer in PDS is driven by convection, the amplitude of the PDS signal decreases as -3/2 (where  is the pulse frequency of “pump” beam) while the amplitude decreases as -1 when heat transfer to the fluid mainly occurs by

conduction. In this second case, the amplitude of the PDS signal immediately provides the thermal capacity of the sample while, in both conduction-driven and convection- driven PDS the phase of the PDS signal provides the thermal diffusivity. We can therefore conclude that, where as PDS is not convection-driven, it is a very useful technique for simultaneously measuring the thermal capacity and thermal diffusivity and, subsequently, the thermal conductivity of ultr-thin films, as will be widely explored in the next chapters of our work.

References

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New York, 10013-2473, USA, 2011.

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Wiley & Sons, New York, 1996.

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Chapter 4

4

Staebler-Wronski effect, thermal conductivity, and self-repair

of hydrogenated amorphous silicon during light-induced

degradation

An introduction to amorphous silicon (a-Si), hydrogenated amorphous silicon (a-Si:H) and experimental methods to grow a-Si:H thin films are presented. The main focus is on the investigation of the effect of light soaking on the optical and thermal properties of a set of a-Si:H thin films. Experimental results reveal that defects that are formed under illumination deteriorate the thermal conductivity of the thin films samples, which in turn leads to a rise in temperature of the samples resulting in self-repair of the defects. A model is proposed to explain the self repair of the defects created in a-Si:H thin films under illumination.

4.1

Introduction

Silicon is the element of choice in electronic and optoelectronics, and more than 90 % of solar cells on the market are based on this element [1]. Therefore, a good test for our photothermal deflection spectroscopy (PDS) apparatus consists in demonstrating its ability to understand the interplay between the optical and thermal properties in solar- grade, silicon-based, thin films. While crystalline silicon is extremely popular as photovoltaic material, amorphous silicon solar cells also have excellent market share due to their cost efficiencies [1,2]. PDS has been extensively utilized to study small optical absorptions in hydrogenated amorphous silicon (a-Si:H) and, historically important processes in understanding the relationship between topological disorder and optical

properties in this material have been achieved by PDS [3,4]. Conversely, investigations of thermal properties of a-Si:H by PDS have been very limited, so far, due to the fact that most PDS apparatuses are designed for and dedicated to studying the optical properties.

In the case of crystalline silicon (c-Si), atoms are arranged in long-range ordered tetrahedral lattice, with four nearest neighbours each. Conversely, in amorphous silicon (a-Si), there is structural disorder due to fluctuations in bond lengths and bond angles. Since deviations of Si-Si bond lengths and bond angles from their values in a perfect tetrahedron are very small, short-range order still exit in a-Si. The covalent bonds between the silicon atoms in a-Si are same as in c-Si. The disorder is represented by the radial distribution function (RDF) which is the probability of finding an atom at a distance r from another atom. Schematic RDF for c-Si and a-Si are shown in Figure 4.1. [5,6]. D. E. Polk [7] showed that the radial distribution function (RDF) in a-Si obtained from electron

Figure 4. 1 Schematic of RDF for c-Si and a-Si adopted from [5,6]. There are well defined peaks for c-Si but for a-Si first peak is clear , second is

broadened and there is no peak after that showing that a-Si lacks long range order.

diffraction experiments show that the first peak matches with that of c-Si but second peak is broadened as compared to c-Si and third peak disappears. Typically, deviations in bond angle and bond length in amorphous silicon are ~ 5% and ~ 1% respectively [2,6].

This fact implies that chemical bonding and coordination number are the same in crystalline Si and in the corresponding amorphous materials. On the other hand, the lack of long-range order has strong implications on the optical and thermal properties of amorphous silicon, which are profoundly different from those of its crystalline counterpart.