運用於微系統設計最佳化之微機電組件結構物理分析

Abstract

機電系統(Micro-Electro-Mechanical Systems，MEMS)是利用微米級立體結構實現感測和執行功能的一項關鍵技術。由於工業技術和經濟的相輔成長，使得微機電元件微型化(Miniaturization)獲得成功、能效得以提升，進而讓設計和應用層面不斷擴大，因此它們在消費性應用市場的普及率正不斷提高。其中，其應用觸角除了大量消費性電子與汽車應用，更伸及微奈米電子工業、醫療、能源、光纖通訊以及航太軍事等專門的應用領域。例如：射頻微機電(RF MEMS)元件優異性能可用於改良手機天線性能或是血糖反應與血壓偵測訊號傳輸，並在醫療影像應用中扮演連結身體各部位器官的角色，因此適合做為研究與商業應用的「人體區域網路(Body-Area Network)」元件。聲學應用層面亦有用於手機的微型麥克風與喇叭、人工電子耳、聲紋分析辨識，以及微型機械人指向元件等。於應用層面中，五種基本且實用的微機電組件結構，例如：螺旋狀結構、鰭狀結構、樞紐與梁的結構、層疊結構，以及傾面結構，業已被設計、利用且與其他微機電元件成功地相互整合。然而，整體性的微機電元件物理分析的缺乏，將導致發展高性能微系統的設計最佳化之困難，特別在於與輔助電路系統方面。為了克服此處的窘境，微機電組件分析物理模型以及其相關的元件或系統性能最佳化，包括射頻微機電式螺旋型電感、複合型鰭狀基底、樞紐形微機電麥克風、層疊光學系統與面射型雷射，以及在矽基板上的倒金字塔型傾面中成長一維材料的方法，皆已在本論文中詳述其物理基礎與最佳化方針。Kramers-Kronig Relations對於共振吸收的數學特性，已被運用於微機電式電感被動元件模型中用以描述電子共振行為；nitride/oxide/nitride/air複合鰭狀結構亦被運用在改善被動元件之基底損耗效應(Substrate Loss Effects)中。此外，一種新穎的中央懸浮結點結構亦被提出，並用於改善傳統微機電聲學結構之靈敏度與指向性。同時為了分析並預測MEMS元件與後端電路上的熱淤積分佈與系統最高溫度，本論文中發展出廣義等效電熱網絡π模型，使結構分析得以簡化並讓模擬運算時間大幅縮減。利用Green’s Theorem對於描述能量流(Energy Flux)的數學特性，本論文中提出了熱傳導、對流以及熱電阻的積分演算式並已經成功用於預測與描述高速光學通訊系統中的熱淤積分佈與最高溫度。亦預見三維奈米電子技術最終將成為有效製做高密度電子產品與MEMS立體元件之利器，本論文中以垂直成長的奈米碳管(Vertical-Aligned Carbon Nanotubes)為例，提出了高效率且可依IC設計者需求而佈局的設計方案：藉由精準控制晶種的大小與位置，來實現奈米碳管的成長位置與其單/多壁(single/multi-wall)特性。最終，本論文以材料與元件結構之觀點，提出了數項重要微機電組件結構之物理模型與分析以及清晰的設計指標，以期待得以實現微系統設計最佳化之目標。

MEMS (Micro-Electro-Mechanical Systems) devices have been the key ingredients for simultaneously realizing sensing and actuating functionalities in a system with a micro-scale structure. Due to the both substantial growth of industrial technologies and economic activities, the successive miniaturization and superior performances of the MEMS devices have extended their application and penetration in the consumer electronics market. The MEMS applications have ranged from the consumer personal portable electronics, vehicle auto-control, medical instrument, power generator, high speed data communication, military weapon, to aerospace voyage, and so on. For instance, RF MEMS passives such as inductor, capacitor, filter, and antenna, etc, have been utilized to enhance the performance of cell-phone transceiver due to their excellent performances in frontend tuning parts. MEMS acoustic components like microphone and loudspeaker have also been adopted in cell phones, cochlear prosthesis, and so on. In the applications, five fundamental and common MEMS component structures, such as spiral, fin, pivot and beam, stacking, and inclined surface structures, have been designed, utilized, and integrated with each other to form MEMS devices. Nevertheless, lock of entirely physical analyses about the devices could result in the difficulty in the design optimization for developing high performance microsystems, especially in the implementation of circuitry design. To overcome the predicaments, the physical analyses of the MEMS components with close-form models and the corresponding optimization in device or system performance including RF MEMS passive spiral inductor, MEMS acoustic pivot-supported microphone, VCSEL in stacked optical system, and seeding control for 1-D material growth using inclined surfaces of an inverted silicon nano-pyramid are presented in this dissertation in detail. The investigation starts with the establishment of a mathematical model to depict the resonant behavior of the MEMS inductors using Kramers-Kronig Relations, and the spiral inductor can be easily and well optimized with high Q and inductance characteristics for RFIC applications. A nitride/oxide/nitride/air composited-fin structure is then presented to improve the substrate loss effects for high speed transmission applications. For sound source localization, a novel central-supported floating joint with central beams used in a hybrid microphone is proposed and presented with an analytical model to enhance the sensitivity and directivity of the conventional MEMS acoustic component structure. The biomimetic microphone design can lead the way to develop the next generation acoustic sensing and tracking microsystems like hearing aids, robots, and bionic military devices. To well analyze and predict the distribution of thermal accumulation and hottest spot occurring in a stacked optical microsystem, a general equivalent eletrothermal network π-model is presented for simplification of the structure and saving the CPU-run-time during simulation. By means of the mathematical approach of Green’s theorem for estimating energy flux inside a heating system, expressions of heat conduction, convection, and thermal resistance in view of integral forms are also presented and applied on the prediction of thermal distribution and hottest spot in a high speed optical data communication system successfully. At final, a precise seeding control scheme of vertical-aligned carbon nanotubes (CNTs) is presented for 3D nanoelectric applications, since the 1D materials have become the next generation candidate for the fabrication of nanoelectronics systems. A seeding control scheme including the physical mechanism of formation is proposed and demonstrated by employing gravitational force to form an agglomeration of melted cobalt seeds on the inclined surface of a patterned inverted silicon nano-pyramid. It is our belief that the presented physical analyses of MEMS component structures and the establishment behavior model between device performance and related material property and geometry in this dissertation can really provide a clear design picture and analytical approach for MEMS designers and engineers to really realize the goals of microsystem optimization.