Award Date


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Committee Member

Hui Zhao

Second Committee Member

Shengjie Zhai

Third Committee Member

Kwang Kim

Fourth Committee Member

Shubhra Bansal

Fifth Committee Member

Yingtao Jiang

Number of Pages



Recently, nano-scaled surface decoration has brought significant advancement and exciting new possibilities to light management. Numerous nanostructure patterns have been explored, wherein the quasi-random nanostructures (QRNs) present a promising path in manipulating light to increase the photon flux over the broadband spectra for optical (e.g., photovoltaic) devices. However, due to the infinite number of QRNs, it is difficult to directly design and fabricate the exact QRN pattern as desired to achieve the optimized light-trapping capability. To overcome this obstacle, we 1) digitize the traditional continuous QRNs into meshes and then map the meshes to binary matrices, which can be deterministically programmable; and 2) introduce the “star discrepancy” to evaluate the QRNs’ degree of the randomness, which can guide the design and further optimization of QRNs to improve the light-trapping capabilities.In this dissertation, two-dimensional (2D) QRNs are generated by filling the matrices with deterministic one-dimensional (1D) binary sequences (i.e., Fibonacci, Rudin-Shapiro, Thue-Morse) in a spiral way or direct binary plots (i.e., Halton (2,3)). Additionally, different heights can be assigned quasi-randomly to the 2D quasi-random pattern to generate a three-dimensional (3D) QRN. Compared to the bare solar cells, the efficiency improvement of the solar cell device with our 2D Fibonacci quasi-random nanostructures arranged in an Archimedean spiral is up to 8.31%. Meanwhile, the reflectance on the surface is tremendously reduced by 11.62% at 800 nm. The results show that either the spiral arrangement of nanostructure or QRNs play the key role in the light-trapping scheme. Besides this, we found that in almost the entire visible light spectrum, a higher degree of the surface randomness (i.e., star discrepancy) indicates a higher antireflection capability. A novel “star discrepancy” calculation is consequently employed in this dissertation to assess the degree of surface randomness (2D) or spatial randomness (3D). Based on the star discrepancy calculation, the optical and electrical performance of the different 2D quasi-random nanostructures can be assessed and optimized without conducting any experiments. Thus, by changing the star discrepancy (i.e., the degree of surface randomness for 2D nanostructure) of RS QRNs, the RS QRNs can be optimized. The two optimized QRNs with drastically increased star discrepancy gradually reduce the surface reflection by up to 25% decrement in the strong reflectance region (~500 nm). Moreover, we found that the 3D QRN design outperforms the 2D QRN design for a nanostructured semiconductor layer of a solar cell by taking the randomized heights into consideration. These different types of 3D QRNs possess a higher degree of spatial randomness by assigning the randomized heights to the nanostructures, which leads to a highest Jsc enhancement of up to 22% compared to slab cell. Furthermore, the 3D QRNs resulted in an omnidirectional and broadband reduction in optical reflectivity. Hence, the integration of the QRN design and star discrepancy evaluation can be employed to various applications, ranging from external anti-reflective coatings to internal broadband light-trapping structures for the semiconductor layers inside optoelectronic devices. We expect that this systematic methodology could be readily applicable to other nanostructures across all length scales, whose performance largely depends on the surface randomness (2D) or even spatial structural distribution (3D).


Light-trapping; Optical disc technology; Programmable binary data; Quasi-random nanostructure; Solar cells; Star discrepancy


Mechanical Engineering

File Format


File Size

5500 KB

Degree Grantor

University of Nevada, Las Vegas




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