奈米級金氧半場效電晶體應變矽物理之研究

Abstract

為了提升MOSFETs元件效能及載子遷移率(carrier mobility)，在(001) 晶圓上的單軸縱向(uniaxial longitudinal)及雙軸(biaxial)應變矽製程已被廣泛的應用在先進的奈米技術中。

在本論文中，首先，為了探討在不同的晶圓方向及不同的應力條件下，是否能進一步的增高元件效能及降低元件功率，我們將應變張量(strain tensor)表示成縱向應力(longitudinal stress)、橫向應力(transverse stress)及垂直應力(normal stress)的函數。接著利用deformation potential theory以及k•p framework來分別計算在三種晶圓方向：(001)、(110)和(111)上及不同的應力條件下，應變矽材料的傳導帶和價電帶的能帶結構(band structure)、能谷位移(band edge shift)、三維k空間下的等能量面(constant energy surface)、二維能量等高線(2D energy contour)，以及有效質量(effective mass)。另外，額外的垂直晶圓方向應力及橫向應力也被考慮及計算。利用以上的計算結果來作為分析的工具，我們發現在這些可能的應變形式中，對nMOSFETs來說，在(001)晶圓上的單軸及雙軸伸張應變具有較佳的增益；而對pMOSFETs來說，在(001)和(110)晶圓上的單軸壓縮應變具有較佳的增益。此外，對pMOSFETs來說，在(001) 晶圓上加上額外的橫向伸張應力可以進一步的增進元件的電導率(conductivity)。

接著，利用計算出來的能帶結構，我們萃取出在(001) 晶圓方向上的單軸及雙軸應變下的量子化有效質量(quantization effective mass)、二維及三維能態密度有效質量(2D and 3D density-of-state effective mass)。此外，根據應變下的能帶結構，我們推導及修正了半導體元件物理中常用的物理表示式，包含材料的費米能階(Fermi energy)、傳導帶及價電帶的有效狀態密度(conduction and valence effective DOS)、本質載子濃度(intrinsic carrier concentration)，使其可以繼續延伸應用到材料內具有應變的情況。同時我們也計算了這些參數在單軸及雙軸應變下從零到3GPa的變化，並提出了合理的物理解釋。以上這些參數在決定材料特性及元件效能時相當重要。

最後，根據以上的討論，我們建立了一套物理模型及模擬器來評估及計算應力對MOSFETs元件造成的影響，包含平帶電壓(flat-band voltage)、應變下對應的多晶矽閘極/氧化層/通道截面能帶圖(band diagram)。並將三角形位能井近似法(triangular potential approximation) 延伸應用到應變矽MOSFETs元件中，同時也考慮閘極及通道均具有應變的情況。此方法可計算出在不同應力條件、外加電壓及元件參數下介面電場、次能階、反轉層載子濃度及多晶矽閘極/氧化層/通道跨壓等重要參數。接著，利用WKB方法，我們也計算出在(001)晶圓上單軸壓縮應變對nMOSFETs和pMOSFETs的閘極直接穿隧電流(gate direct tunneling current) 的影響，模擬結果與實驗數據吻合。

In this work, by using the deformation potential theory for conduction band and the k•p framework (6 6 Luttinger Hamiltonian) for valence band, the strain-altered band structure (E-k relation), the strain-induced band edge shift, the constant energy surface, and the 2D energy contour have been calculated for various stress conditions on three conventional wafer orientations, (100), (110), and (111). Moreover, the influences of the additional transverse or normal strain have been examined as well.

Next, utilizing the calculated E-k relation, the conventional physical parameters including the quantization effective mass, the 2D DOS Effective mass, and 3D DOS effective mass have been also extracted under uniaxial and biaxial stress on (001) wafer. Then, using the DOS effective masses and strain-induced band edge shifts, the Fermi energy of bulk silicon can be determined as a function of stress and doping concentration. These parameters are significant in calculating the subband energy and carrier density in the channel inversion layer of MOSFETs. In addition, we also evaluated the intrinsic carrier density of bulk silicon under uniaxial and biaxial stress from zero to 3GPa.

Furthermore, we extended and modified the previously developed triangular potential approximation, a self-consistent method that takes the quantum confinement effect in the inversion layer and the conservation of electric flux at the SiO2/Si interface into consideration, for the unstrained MOSFETs to construct the band diagram and physical model for strained counterparts. The method has also been applied to both nMOSFETs and pMOSFETs with corresponding revisions of the physical model. In our model, the stresses for poly gate and channel are allowed to have different magnitude and type.

Finally, applying our model and the extracted physical parameters, we can calculate the interface electric field, subband energy, inversion carrier density, substrate band bending, etc., with various stress conditions, applied voltage and device parameters as inputs. Then, utilizing the WKB approximation, the transmission probability and gate direct tunneling current for various stress conditions can also be evaluated. The simulated results agree with the experimental data of the former works.