https://scholars.lib.ntu.edu.tw/handle/123456789/81354
Title: | 應力下因表面能及彈性能變化造成孔洞變形之研究 | Authors: | 陳兆勛 | Issue Date: | 31-Jul-2005 | Publisher: | 臺北市:國立臺灣大學應用力學研究所 | Abstract: | 隨著ULSIC’s(Ultra-Large-Scale Integrated circuits)技術的進步,半導體元件已進入次微米 (sub-micron)時代,其中鋁金屬載線(interconnect)廣泛使用於元件結構。因此載線的可靠度對於產品 元件壽命有很大的影響。 在過去的文獻及實驗中發現,鋁金屬載線元件於高溫下受到大電流、熱應力的交互作用下,載線內 部的原子會因為能量的變化而產生擴散飄移的現象。若此時載線內部存在一孔洞(viod),其可能為自然 缺陷,也可能由原子擴散飄移而生成,進而移動、成長,則孔洞會因表面的原子擴散造成孔洞形變,進 一步產生裂縫尖端。一旦裂縫尖端應力超過臨界值,鋁金屬載線會因孔洞裂縫的快速劈裂而破壞,甚至 切斷載線,形成斷路(open failure),失去原有的元件功能。 我們試圖使用原子等級精確度且可變溫的掃描探針顯微術(STM)來觀察奈米金線與在矽表面成長的 奈米島,試圖了解電子在奈米材料中的量子現象。我們的實驗主要是觀察金屬吸附在矽表面的二維結構 排列變化。相的結構排列變化,主要是電子效應。我們觀察相轉變中間過程,發現到單原子缺陷周圍有 電子結構,並且由於電子效應使得單原子缺陷在表面形成週期性的排列分布而產生不同之相變化。另參 考Wang[4], Suo et al.[25]與Wang[26]以孔洞表面擴散方式為基礎,並加入Asaro 與Tiller[22]的化學能理 論,針對圓形孔洞變形成狹長型裂縫的過程,提出二維尺度模型分析。將統御方程式導入伽遼金法 (Galerkin approximation method),以求得金屬載線孔洞形狀穩定的臨界應力值大小,以及其對於載線壽 命的關聯性。 本研究乃根據Wang[4]文獻,並加入Wu[27]對於化學能的修正項,假設載線材料為彈性材料,且僅 只限分布於孔洞表面的原子參予擴散機制。孔洞變形過程中會引起表面能(surface energy)與彈性能 (elastic energy)變化,將能量變化改變量相比較,若以表面能變化為主,孔洞變形會達到一平衡狀態, 形狀為橢圓型;若以彈性能變化為主,孔洞變形將無法達到平衡狀態,且會產生裂縫尖端。 利用等角映射法(conformal mapping method)以一級數描述孔洞形狀,再以對應的級數係數變化來 表示孔洞的動態變形過程。此外,利用複變方法(complex variable method)求得孔洞周圍的彈性場與位 移場分佈。 將統御方程式導入伽遼金法(Galerkin approximation method),以求得鋁金屬載線孔洞形狀穩定的臨 界應力值大小,以及其對於載線壽命的關聯性。此外,對於孔洞裂縫尖端生成需要時間、裂縫尖端大小、 裂縫尖端應力集中、材料及應力作用的非等向性等影響,也將一併討論之。 Semi-condoctor industry has entered sub-micron age with the progress of ULSIC’s technology. Since aluminum interconnects are widely applied to semi-conductor devices, its reliability has great influence on lifetime of product devices. From the past references and experiments, we found that as devices with aluminum interconnects are affected by the interaction of intense electric currents and thermal stress at high temperature, energy variation will bring about atomic diffusion inside aluminum interconnects. In the meanwhile, if there is a void, which could be an original defect or nucleates owing to atomic diffusion and keeps drifting and enlarging, inside the aluminum interconnect, pore shape change and then crack tips will be forming due to atomic diffusion on the surface of the void. As soon as stress of crack tips exceeds the threshold, aluminum interconnects will be broken and even cut off as a result of fast fracture of crack tips, which will form open failure and defunction devices. According to the references, we propose the hypothesis that interconnects are made of elastic materials and diffusion only take places on atoms distributing on the surface of voids. And we found that surface energy and elastic energy will vary during the process of pore shape change. If surface energy variation dominates, pore shape change will achieve the state of equilibrium in the form of ellipse. Otherwise, pore shape change will not achieve the state of equilibrium but cause crack tips instead. We will apply the Conformal Mapping Method to describe pore shapes by using power series. And how the corresponding coefficients of power series vary will indicate the process of dynamic evolution of pores. Besides, the distribution of elastic field and displacement field around the pore can be acquired by Complex Variable Method. We will substitute governing equation for Galerkin Approximation Method to acquire the threshold value of stress of a pore in a state of a stable shape, and observe how these values relate to lifetime of interconnects. Furthermore, the time it takes to nucleate crack tips, the size of crack tips, the stress concentration factors of crack tips, and anisotropy of materials and stress will be discussed later. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/21745 | Other Identifiers: | 932212E002069 | Rights: | 國立臺灣大學應用力學研究所 |
Appears in Collections: | 應用力學研究所 |
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