三維多體陷阱模擬

Abstract

本論文旨在探討三維多體陷阱(殘缺分子鍵結、量子點、浮動閘極等)之模擬。研究主題主要與數值分析與元件模擬器相關。於本論文中探討之方法主要不僅是為了因應可能即將來到之十數奈米節點(1X nanometer)之元件微縮，在一般使用在元件方面的材料亦小心調查。尤其在絕緣體中，”陷阱”本身並不與泊松方程式之邊界條件相連，因此，有個特別的演算法因應而生[1]。這也使得該演算法可適用在探討可靠度議題上之一般目的之元件模擬器[2]。姚智偉在模擬微浮動體之庫倫阻斷[4]時，以Kick演算法[3]重現了部分程式之功能，並模擬了在陷阱協助下之穿隧效應與隨機電報雜訊[5]。然而，該次的模擬只針對單一微浮動體重現，而在原本的版本[2]中，能重現雙體之一般目的元件模擬。在本論文中 ，我們以至少三體浮動體為目標來擴展kick演算法，藉由下列在[3]，[4]上得到之進展： 1. 透過有限體積法網格切割 2. 電子元件表現在不同材料邊界上的改善 3. 擴展單電子精度於多點浮動體上 首先，我們呈現了網格切割上的進步對於計算時間與記憶體量的減少。為了驗證網格切割上的進步，我們實際模擬單一微浮動體並確認電子精準度與計算時間。第二，在表現不同材料邊界上，也實際展示了全三維單一微浮動體模擬。最後，我們重構了單一微浮動體精度程式並能呈現多點浮動體模擬 。為了這個目標，我們從單一微浮動到多點浮動體，擴展了kick演算法 。於此，我們同時也建構數學模型，研究kick演算法並探討其是如何減少計算時間。

This thesis is focusing on the fully three dimensional (3D) simulation with multiple floating islands (i.e., traps, dangling bonds, quantum dots, floating gates, and so forth). The research topics are related to numerical analysis and device simulator. The method that will be discussed here is applicable not only to simulate advanced electron devices (beyond 1X nanometer) but also to carefully investigate materials daily-used in electron devices. Since those floating islands are not connected to any boundary that is necessary to solve the Poisson equation, a unique algorithm was developed [1]. And hence, this algorithm was used in general-purpose device simulator for investigating the reliability issues of real-life electron devices [2]. Chi Wei Yao reproduced a part of this program as Kicking Algorithm [3]; which was used to simulate Coulomb Blockade of very small floating dot [4] and Trap-Assisted Tunneling (TAT) and Random Telegraph Noise (RTN) of high-K dielectric [5]. However, this reproduction was done for sole floating island, while the original program used in [2] was available to two floating islands in general-purpose device simulation. In this thesis, we expand the Kicking Algorithm to be applicable to at least three floating islands by the following improvements from [3], [4]: 1. Meshing by Finite Volume Method (FVM); 2. Improvement of the ability of representing boundaries between different materials/regions in electron devices; 3. Expansion of Single Electron Sensitivity (SES) to multiple floating islands; Firstly, we show that an improved meshing method can reduce the computational time and the memory load. To validate the improved meshing method, we apply it to carry out the device simulation with a sole floating island for checking the accuracy and the computational time. Secondly, the ability of representing boundaries between different regions is also investigated by demonstrating the fully 3D device simulation with sole floating island. Finally, we re-construct the code of the single electron sensitivity that has been developed in our group for making it applicable to multiple floating islands. In other words, the kicking algorithm method is expanded from single floating island to multiple floating islands. A mathematical model is also produced to investigate how to improve the computational speed.