隨著互補式金氧半場效電晶體(CMOS)尺寸的微縮，衍伸出許多需要進一步探討的議題。本論文中採用了非平衡態格林函數(NEGF)求解薛丁格方程式的方法描述在奈米尺寸雙閘極金氧半場效電晶體中，電子的量子傳輸行為，同時藉由將此傳輸方程式與波松方程式求得收斂的自相一致電位值，求得電子密度、傳輸係數及電流，並由此得到閘極電壓與汲極電流的關係曲線。

量子效應已包含在於電子傳輸方向使用NEGF方法及求解厚度方向(量子侷限方向) 的薛丁格方程式中。除此之外，當元件尺寸夠小，矽本體厚度夠薄時，在厚度方向，實驗上量測到的介電常數值會較塊材為小，理論計算上的預測，為介電質張量(電容率張量)，對角線的元素中，描述厚度方向的矩陣元素較塊材為小，矽本體為一非等向性介電質。另一個已提出的模型是，沿著厚度方向，從材料中央到表面，介電常數從塊材的介電常數值逐漸下降，電容率的分佈隨空間而變化，矽本體為一非均勻性介電質。本論文目的旨在探討當矽本體為非等向性介電質及非均勻性介電質時，其電性和當矽本體為一般塊材(為一等向性及均勻介電質)時的差異。

由計算結果得知，當表面區域的介電常數(電容率)下降時，由於在電子傳輸方向的能障增加，使得在相同偏壓下的電流變小，元件的次臨界擺幅降低且臨界電壓增加，因此較不會受短通道效應的影響。而當在厚度方向(量子侷限方向)的介電常數(電容率)下降時，由於在電子傳輸方向的能障降低，使得在相同偏壓下的電流變小，因此元件的次臨界擺幅增加且臨界電壓上升，較會受短通道效應影響。

對於長通道元件而言，介電常數(電容率)的變化對於電子傳輸方向之能障的影響較不明顯，因此當介電常數(電容率)下降時，對I-V曲線的影響幾乎可以忽略。

CMOS scaling has led to several issues that are necessary to be investigated further. In this thesis, the transport behavior of electrons in a nanoscale double-gate (DG) MOSFET is modeled by solving Schrödinger equation in non-equilibrium Green’s function (NEGF) formalism which is solved self-consistently with the Poisson equation to obtain the potential profile, electron density, transmission coefficient and thus, the drain current versus gate voltage (I_DS-V_GS) curves.

In addition to quantum effects which have been taken into account in the transport equation, the reduction of permittivity in the surface region and the anisotropic permittivity that influence the electrical properties are investigated and their influences on the electrical characteristics of MOSFETs are discussed.

It is shown that the reduction of permittivity in the surface region slightly improves the subthreshold swing and slightly increases the threshold voltage due to the increase of the potential barrier for electrons in the transport direction. This suggests the better immunity to SCEs for materials of the channel with smaller permittivity. In the case of anisotropic permittivity, the subthreshold swing degrades and the off-leakage current becomes higher as the permittivity in the confinement direction becomes smaller due to the decrease of the potential barrier in the transport direction. This suggests the better immunity to SCEs for materials of the channel with larger permittivity in the confinement direction.

For long channel devices, the variation in permittivity barely changes the potential barrier in the transport direction. Therefore, the variation in the permittivity has neglecting effects on the (I_DS-V_GS) characteristic.

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