最近的實驗觀察到在STO/LAO界面上出現二維電子氣 (2DEG) 的情形，此項發現已經吸引了許多實驗和理論上的關注。在這一篇論文中，我們首先以數值方法探討在此界面的二維電子氣形成的機制。部分的電子是來自於LAO上的缺陷，因為界面 (interface) 位能差異而轉移到STO，在LAO/STO界面上形成二維電子氣。更近的一篇報導指出：若在STO/LAO外加上一層PZT，則二維電子氣的濃度可以因PZT的極化方向而增加或減少。為了解釋這個實驗所觀察到的現象，我們建構了一個模型：A .因為LAO/PZT界面的不平整 (roughness)，引起迷走電場 (stray field) 延伸到STO/LAO界面；B.迷走電場改變STO的雜質所看到的電場而產生極化場，使得部分STO的位能高於費米能帶 (Fermi energy)，這一部分改變了二維電子氣的密度大小。

Recent reports about the existence of two-dimension electron gas (2DEG) at the interface between STO/LAO had attracted many experimental and theoretic interests. In this thesis, we first numerically demonstrated the formation of 2DEG. A charge transfer from the impurities in LAO to STO builds the fundamental electric field at the interface for the setup of 2DEG. A most recent report showed that the concentration of 2DEG in STO/LAO/PZT hetero-structure could be enhanced or suppressed by the direction of polarization in PZT cap layer. To explain this experimental observation, we first built a model for obtaining leaking field from the PZT bound charge due to interface roughness. Then, the leaking field changed the resultant potential profile near the interface, and polarized the impurities in the STO layer. The non-uniform polarization yields an extra bound charge distribution, which produces a bump potential profile in STO layer and therefore changes the concentration of 2DEG.

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