標題: n型反置層精準量子計算:應變、次能帶、遷移率及三維結構
Sophisticated Quantum Computation on n-type Inversion Layers: Strain, Subband, Mobility, and 3-D Structure
作者: 李韋漢
Lee, Wei-Han
Chen, Ming-Jer
關鍵字: 應變;次能階;遷移率;三維應力;Strain;Subband;Mobility;3-D Stress
公開日期: 2012
摘要: 根據莫爾定律法則,我們正走向22/20奈米的科技世代,而且會不停地繼續開發更新更有效率的元件。然而在前進的路上會遇到許多問題,其中一個值得注意的問題是應力效應,它會影響到元件的一些電性和製程上的問題。這些物理特性我們可以從對漏電流和電子遷移率的實驗及模擬上觀察到。此外閘極穿隧電流跟次能階高度和位能障等能帶結構有強烈的相關性。所以閘極穿隧電流是個找次能階和應力效應的好工具。要建立一個正確的n型轉置層模擬計算,我們從對閘極穿隧電流的數據去做匹配的動作,接著是遷移率的計算,最後完成一個全面性的計算工作。 能帶結構計算和遷移率量測在最近被用來評估在場效電晶體中等效質量隨著應變之下的變化係數。在此論文中,我們提出一個新的實驗方法,乃藉由對<110>方向上的壓縮應變改變 (001) n型金氧半場效電晶體的閘極直穿隧電流做匹配動作。這個方法的重點是直穿隧的機制對在等效質量隨著應變之下的變化係數非常敏感,因為變化係數可以影響到次能階的位置。在此,我們使用了一個以三角位能近似的架構的模擬器。為了達到更精確的成果,我們提出了一個修正係數的演算法去補償使用三角位能近似法解出次能階計算上的誤差。接著用已知的形變位能常數和單向壓縮應力作為輸入的條件,帶有應力效應的量子模擬器就完成了。模擬器計算出的閘極直穿隧電流被用來與實驗比較,因此帶出兩谷和四谷的等效質量隨應變下變化係數的值。其值也跟被發表在文獻的值作比較。 在我們以實驗的方法,透過應力誘發閘極穿隧電流增益,去萃取二維電子氣的等效質量隨應變的變化係數,結果指出導帶中垂直平面方向上(量子侷限)四谷的等效質量隨應變的變化係數是存在的。為了更確定這個事情,在此我們提供了另一個證據。首先,我們針對幾種不同的等效質量隨應變的變化係數的值作為明確的方針。接著,我們採用一個可計算應力和量子效應的自洽的模擬器去執行同時對文獻上在單向拉伸應力的實驗情形下遷移率增加和閘極電流減少作個匹配。發現在能帶計算上忽略了垂直平面方向上四谷的等效質量隨應變的變化係數只會做出很差的匹配結果。 在模擬器結構被建立且可信之下,可使我們的工作延伸到其他情況。除了之前的(001) 平面, (110) 和 (111) 的平面場效電晶體中次能階和遷移率的計算也可以用以估計在應力工程下的傳輸特性。穿隧效應在元件微縮下顯得越重要。為了要對三維結構,像是鰭狀場效電晶體的電性做些實驗,雙閘極場效電晶體結構的次能階計算可以直接的達成。計算結果也顯示出在薄基板厚度下特別易有穿隧效應。同樣地,在不同平面不同通道方向的元件時,應力影響遷移率的變化也可以被估計出來。
Following Moore’s law, we are currently entering into the technology generation of 22/20 nm and will keep developing newer and more efficient devices. We will encounter many problems in this long road. Stress engineering is one of the noticeable candidates due to significant changes in electrical performance and process issues. By fitting to the data of leakage current and electron mobility, some physical mechanisms can be brought out. On the other hand, the gate direct tunneling correlates strongly with the band structure, such as the subband energy level and barrier height. Thus, the gate direct tunneling could be a good tool to detect the subband level and hence the effect of stress. To build a correct computation of n-inversion layer in our simulator, this work starts with the fitting to gate direct tunneling data, followed by the mobility calculation brought out in the next step and finally the comprehensive computational work. Currently, both the band-structure calculation and the mobility measurement are used to assess the electron piezo-effective-mass coefficients in strained nMOSFETs. In this work, we present a new experimental method through a fitting of the strain-altered electron gate direct tunneling current of (001) n-channel metal–oxide–semiconductor field effect transistors under <110> uniaxial compressive stress. The core of this method lies in the sensitivity of the direct tunneling to the position of the subband level in the presence of the electron piezo-effective-mass coefficients. Here, a simulator based on triangular potential approximation is utilized. To make more accurate calculation, we proposed a new algorithm that a correction-coefficient generating expression is systematically constructed to compensate for the error in the subband levels due to the use of a triangular potential approximation. Then, with the known deformation potential constants and uniaxially compressive stress in the channel as inputs, a strain quantum simulator is carried out. The resulting gate direct tunneling current is used to fit experimental data, thus leading to the values of the piezo-effective-mass coefficients associated with the twofold and fourfold valleys. The comparison of the extracted piezo-effective-mass coefficients with those published in the literature is made. After we have experimentally extracted the piezo-effective-mass coefficients of 2-D electrons via the stress-induced gate tunneling current enhancement, the results pointed to the existence of a piezo-effective-mass coefficient around the fourfold conduction-band valley in the out-of-plane (quantum confinement) direction. To strengthen this further, here, we provide extra evidence. First, explicit guidelines are drawn to distinguish all the piezo-effective-mass coefficients. Then, a self-consistent strain quantum simulation is executed to fit literature data of both the mobility enhancement and gate current suppression in the uniaxial tensile stress situation. It is found that neglecting the fourfold-valley out-of-plane piezo-effective-mass coefficient, as in existing band structure calculations, only leads to a poor fitting. As the structure of our simulator is built and valid, our work could extend to other cases. In addition to (001) case, the subband and mobility calculation in (110) and (111) planar MOSFETs can accountable the transport characteristics under strain. The effect of wave-function penetration is significant as the device is scaled. To examine the electrical characteristics in 3-D structures device such as FinFETs, the subband calculation in double-gate structures can be straightforwardly achieved. The results exhibit the penetration effect especially in thin silicon films. Again, the stress-induced mobility variations can be estimated for devices with different channel directions and different surface orientations.
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