次臨界區奈米級金氧半場效電晶體之隨機擾動訊號振幅統計分佈引致臨界電壓偏移之建模化

Abstract

有關於電子在金氧半場效電晶體(MOSFET)中的捕捉和釋放，亦可稱為隨機擾動訊號(RTS)等現象，一直以來對於奈米級半導體元件的差異性都是一個重要的議題。最近三維電腦輔助設計之模擬廣泛的運用在隨機擾動訊號之探討上。在次臨界區域以及低汲極電壓下，缺陷的位置將會對應一個ΔId/Id的大小。主要有兩個ΔId/Id分佈:一個是勾勾形狀，在均勻的通道情況下；另一個是尾端延伸形狀的分佈，在不均勻通道下。尾端延伸形狀的分佈是根據以前提出的公式 〖∆I〗_d/I_d =(I_loc/I_d )^2 ，這邊Iloc是指在缺陷附近的電流。我們提出的模型可以重建勾勾形狀的分佈，透過少量的電流模擬在 35x35 nm2 元件中，建構出〖∆I〗_d/I_d 對應每個缺陷位置。這個模型是封閉的。其實為了I_loc/I_d 的實際應用,我們需要來將重要的準則建立起來。若要更深入研究，我們還可以將臨界電壓之變化的分佈變由不同的操作電壓，分別從臨界和反轉層。通道寬度效應可以藉由在勾勾形狀分佈中考慮寬度效應。重要的是，我們模型的使用可以改善很多在實驗統計上或是模擬上的缺點。

The trapping and detrapping of an electron at the SiO2/Si interface of metal-oxide-semiconductor field effect transistor (MOSFET), which is known as random telegraph signals (RTS), has been an important issue for the variability of the nanoscale device. Recently, 3D-technology aided design (TCAD) simulations have been widely used for RTS topics. The trap positions in the channel will have its corresponding ΔId/Id magnitude in the subthreshold region at a low drain voltage. There are two distinct ΔId/Id distributions: a headed one for the percolation-free channel and a tail one for the percolative channel. The tail distribution can be described by using a literature formula 〖∆I〗_d/I_d =(I_loc/I_d )^2, where Iloc is the local current around the trap. Our proposed model can reproduce headed distribution through few 3D-TCAD simulations on 35x35 nm2 channel to obtain the Id/Id for each trap position. The model is in closed form, and the key criteria are drawn from the model for the use of I_loc/I_d formula. Furthermore, the threshold voltage shift distributions can be transformed from the tail distributions, from subthreshold to inversion. The channel width effect can be included through applying the width effect into our headed distributions. Importantly, the use of the analytic model can overcome the disadvantage of statistical experiments or simulations.