Some considerations about Lambert W function-based nanoscale MOSFET charge control modeling

IF 1.4 4区 物理与天体物理 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
A. Ortiz-Conde , V.C.P. Silva , P.G.D. Agopian , J.A. Martino , F.J. García-Sánchez
{"title":"Some considerations about Lambert W function-based nanoscale MOSFET charge control modeling","authors":"A. Ortiz-Conde ,&nbsp;V.C.P. Silva ,&nbsp;P.G.D. Agopian ,&nbsp;J.A. Martino ,&nbsp;F.J. García-Sánchez","doi":"10.1016/j.sse.2025.109080","DOIUrl":null,"url":null,"abstract":"<div><div>The unwanted low-level doping present in supposedly undoped MOSFET channels has a significant effect on charge control and Lambert W function-based inversion charge MOSFET models, as well as on subsequent drain current models. We show that the hypothetical intrinsic MOSFET channel approximation, often used to describe a nominally undoped channel, produces significant errors, even for the low-level concentrations resulting from unintentional doping. We show that the traditional charge control model, which mathematically describes the gate voltage as the sum of one linear and one logarithmic term of the inversion charge, is only valid for the hypothetically intrinsic case. However, it may still be used for nominally undoped but unintentionally low-doped channel devices within the region of operation where the majority carriers are the dominant charge. With this in mind, we present here a better approximation of the nominally undoped MOSFET channel surface potential. We also propose an improved modified expression that describes the gate voltage as the sum of one linear and two logarithmic terms of the inversion charge. A new approximate drain current control formulation is also proposed to account for parasitic series resistance and/or mobility degradation. The new model agrees reasonably well with measurement data from nominally undoped vertically stacked GAA Si Nano Sheet MOSFETs.</div></div>","PeriodicalId":21909,"journal":{"name":"Solid-state Electronics","volume":"225 ","pages":"Article 109080"},"PeriodicalIF":1.4000,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Solid-state Electronics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0038110125000255","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0

Abstract

The unwanted low-level doping present in supposedly undoped MOSFET channels has a significant effect on charge control and Lambert W function-based inversion charge MOSFET models, as well as on subsequent drain current models. We show that the hypothetical intrinsic MOSFET channel approximation, often used to describe a nominally undoped channel, produces significant errors, even for the low-level concentrations resulting from unintentional doping. We show that the traditional charge control model, which mathematically describes the gate voltage as the sum of one linear and one logarithmic term of the inversion charge, is only valid for the hypothetically intrinsic case. However, it may still be used for nominally undoped but unintentionally low-doped channel devices within the region of operation where the majority carriers are the dominant charge. With this in mind, we present here a better approximation of the nominally undoped MOSFET channel surface potential. We also propose an improved modified expression that describes the gate voltage as the sum of one linear and two logarithmic terms of the inversion charge. A new approximate drain current control formulation is also proposed to account for parasitic series resistance and/or mobility degradation. The new model agrees reasonably well with measurement data from nominally undoped vertically stacked GAA Si Nano Sheet MOSFETs.
基于Lambert W函数的纳米MOSFET电荷控制建模的一些思考
在假定未掺杂的MOSFET通道中存在的不需要的低水平掺杂对电荷控制和基于Lambert W函数的反转电荷MOSFET模型以及随后的漏极电流模型具有显著影响。我们表明,通常用于描述名义上未掺杂沟道的假设的固有MOSFET沟道近似会产生显着的误差,即使对于无意掺杂导致的低浓度也是如此。传统的电荷控制模型将栅极电压数学地描述为反转电荷的一个线性项和一个对数项的和,这只适用于假设的固有情况。然而,它仍然可以用于名义上未掺杂但在大多数载流子为主导电荷的操作区域内无意中低掺杂的通道器件。考虑到这一点,我们在这里给出了名义上未掺杂的MOSFET沟道表面电位的更好近似。我们还提出了一个改进的修正表达式,将栅极电压描述为反转电荷的一个线性项和两个对数项的总和。一个新的近似漏极电流控制公式也被提出,以考虑寄生串联电阻和/或迁移率退化。新模型与名义上未掺杂垂直堆叠GAA硅纳米片mosfet的测量数据相当吻合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Solid-state Electronics
Solid-state Electronics 物理-工程:电子与电气
CiteScore
3.00
自引率
5.90%
发文量
212
审稿时长
3 months
期刊介绍: It is the aim of this journal to bring together in one publication outstanding papers reporting new and original work in the following areas: (1) applications of solid-state physics and technology to electronics and optoelectronics, including theory and device design; (2) optical, electrical, morphological characterization techniques and parameter extraction of devices; (3) fabrication of semiconductor devices, and also device-related materials growth, measurement and evaluation; (4) the physics and modeling of submicron and nanoscale microelectronic and optoelectronic devices, including processing, measurement, and performance evaluation; (5) applications of numerical methods to the modeling and simulation of solid-state devices and processes; and (6) nanoscale electronic and optoelectronic devices, photovoltaics, sensors, and MEMS based on semiconductor and alternative electronic materials; (7) synthesis and electrooptical properties of materials for novel devices.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信