International Journal of Photoenergy

Volume 2019, Article ID 1476217, 9 pages

https://doi.org/10.1155/2019/1476217

## Influence of Surface Morphology on Absorptivity of Light-Absorbing Materials

Correspondence should be addressed to Yong Lv; nc.ude.utsib@gnoyvl

Received 28 March 2019; Accepted 30 May 2019; Published 8 September 2019

Academic Editor: Jiangbo Yu

Copyright © 2019 Chunhui Niu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Absorptivity of three kinds of surface morphology, i.e., V-type groove surface, sinusoidal surface, and random distribution, is investigated using a rigorous electromagnetic theory and a finite element method. Influences of surface contour parameters (span distance, intersection angle, and height) and light wave parameters (incident angle and wavelength) on absorptivity are numerically simulated and analyzed for the three kinds of surfaces, respectively. Absorbing spectra about three silicon wafers with different surface roughness are recorded, and the results are coincident with simulated results.

#### 1. Introduction

Improving absorptivity of light-absorbing materials is very significant in laser machining, solar cell manufacturing, and light-sensitive detector fields, wherein surface morphology and surface roughness become one major factor of influencing material absorptivity. When heat treatment is with a laser beam, a metallic material with a smooth surface has only less than ten percent absorptivity to laser [1], and absorptivity of nonmetallic materials relates to the incident angle of laser beam, which is affected by material surface roughness [2, 3]. For metallic and nonmetallic materials, its absorptivity can be heightened through adjusting material surface roughness due to increased light reflected and absorbed a number of times. Solar cell can transfer radiation energy to electrical energy, and its absorptivity is one of the most important performance parameters. Many methods can be used to enhance absorptivity to solar light, e.g., overlaying a surface layer with high absorptivity [4–6], doping with metal nanoparticles to motivate surface plasma polarization excimer [7–9], and controlling surface morphology [10–14]; here, improving surface roughness is a very effective method. Furthermore, to improve the performance of a solar radiometer, some black coating material with high absorptivity is overplayed on the surface and its surface roughness is changed [15]. Therefore, investigating the relationship between material absorptivity and surface roughness of light-absorbing materials is significant.

Li et al. [15] and Su et al. [16] have analyzed the light absorbing ability of several materials with different types of a surface morphology-based light ray tracing method and achieved some common characteristics of improving light absorptivity through changing surface morphology and derived a relationship formula between absorptivity and surface morphology parameters. Chen et al. [17] have equivalently dealt with surface contour line and established a computational model of influence of surface roughness on laser absorptivity using a light ray tracing method and provided a more convenient method for calculating laser absorptivity in a laser heat treatment field.

However, the light ray tracing method is based on a hypothesis that light propagates along a straight line, which is only valid when the characteristic structure dimension of surface morphology of absorbing material, e.g., the period of a microstructure and span of random fluctuation, is far greater than incident light wavelength. But the majority of surface random fluctuations of a common material belong to a micrometer magnitude order and are close to visible light wavelength; therefore, the light ray tracing method is not suited to calculate the absorptivity of a rough surface.

In this thesis, a rigorous electromagnetic theory is adopted to analyze the influence of surface morphology and surface roughness on material absorptivity. COMSOL Multiphysics, which is a commercial software and can be utilized to numerically solve partial differential equations based on a finite element analysis method, is used to solve Maxwell’s equations and simulate the absorbing effect of the rough surface to light. The absorptivity of the three kinds of surface contour profiles such as the V-type groove structure, sinusoidal wave structure, and random fluctuation structure is numerically calculated, and relationship curves between light absorbing performance and surface morphology parameters are obtained. At last, absorbing spectra of three silicon wafers with different surface roughness are measured, and the results are basically consistent with the numerical simulation results.

#### 2. Shortcoming of a Light Ray Tracing Method

Optical wave is a kind of electromagnetic wave in nature, and its propagation obeys Maxwell’s equations, which can be expressed as
where **E** and **D** represent the electric intensity vector and electric displacement vector, respectively, and have a relationship as , where is the dielectric constant. **H** and **B** are the magnetic intensity vector and magnetic induction intensity vector, respectively, and have a relationship as , where is the magnetic permittivity. Furthermore, **J** is the current density, and , where represents the electrical conductivity.

A harmonic plane wave can be expressed as where is the circular frequency, depicts the wave vector in vacuum, and represents the optical path length and is a real scalar function.

Supposing that light wavelength can be approximated to an infinitely small quantity, an equation can be deduced as , where represents the refractive index of propagation medium. For an isotropic and homogeneous medium, it can be derived from the equation that light wave propagates along a straight line.

As mentioned above, the light ray tracing method is valid only when three conditions are satisfied: (1) a harmonic wave, (2) , and (3) .

If a monochromatic plane wave is incident on a material with a smooth and infinite surface, as shown in Figure 1, according to the Fresnel formula [18], the reflectance can be expressed as where is the material refractive index, is the light extinction coefficient, and is the incident angle. If the thickness of the absorbing material is enough to absorb all the transmission light, absorptivity of the absorption material to the incident light can be expressed as .