Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters
In this study, threshold voltage (<i>V</i><sub>th</sub>) variability was investigated in silicon nanowire field-effect transistors (SNWFETs) with short gate-lengths of 15–22 nm and various channel diameters (<i>D</i><sub>NW</sub>) of 7, 9, and 12 nm. L...
| Main Authors: | , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-05-01
|
| Series: | Nanomaterials |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-4991/12/10/1721 |
| _version_ | 1797497316570038272 |
|---|---|
| author | Seunghwan Lee Jun-Sik Yoon Junjong Lee Jinsu Jeong Hyeok Yun Jaewan Lim Sanguk Lee Rock-Hyun Baek |
| author_facet | Seunghwan Lee Jun-Sik Yoon Junjong Lee Jinsu Jeong Hyeok Yun Jaewan Lim Sanguk Lee Rock-Hyun Baek |
| author_sort | Seunghwan Lee |
| collection | DOAJ |
| description | In this study, threshold voltage (<i>V</i><sub>th</sub>) variability was investigated in silicon nanowire field-effect transistors (SNWFETs) with short gate-lengths of 15–22 nm and various channel diameters (<i>D</i><sub>NW</sub>) of 7, 9, and 12 nm. Linear slope and nonzero y-intercept were observed in a Pelgrom plot of the standard deviation of <i>V</i><sub>th</sub> (σ<i>V</i><sub>th</sub>), which originated from random and process variations. Interestingly, the slope and y-intercept differed for each <i>D</i><sub>NW</sub>, and σ<i>V</i><sub>th</sub> was the smallest at a median <i>D</i><sub>NW</sub> of 9 nm. To analyze the observed <i>D</i><sub>NW</sub> tendency of σ<i>V</i><sub>th</sub>, a novel modeling approach based on the error propagation law was proposed. The contribution of gate-metal work function, channel dopant concentration (<i>N</i><sub>ch</sub>), and <i>D</i><sub>NW</sub> variations (WFV, ∆<i>N</i><sub>ch</sub>, and ∆<i>D</i><sub>NW</sub>) to σ<i>V</i><sub>th</sub> were evaluated by directly fitting the developed model to measured σ<i>V</i><sub>th</sub>. As a result, WFV induced by metal gate granularity increased as channel area increases, and the slope of WFV in Pelgrom plot is similar to that of σ<i>V</i><sub>th</sub>. As <i>D</i><sub>NW</sub> decreased, SNWFETs became robust to ∆<i>N</i><sub>ch</sub> but vulnerable to ∆<i>D</i><sub>NW</sub>. Consequently, the contribution of ∆<i>D</i><sub>NW</sub>, WFV, and ∆<i>N</i><sub>ch</sub> is dominant at <i>D</i><sub>NW</sub> of 7 nm, 9 nm, and 12, respectively. The proposed model enables the quantifying of the contribution of various variation sources of <i>V</i><sub>th</sub> variation, and it is applicable to all SNWFETs with various <i>L</i><sub>G</sub> and <i>D</i><sub>NW</sub>. |
| first_indexed | 2024-03-10T03:16:38Z |
| format | Article |
| id | doaj.art-c9aef8cbfc3f432f809b3c835be24426 |
| institution | Directory Open Access Journal |
| issn | 2079-4991 |
| language | English |
| last_indexed | 2024-03-10T03:16:38Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Nanomaterials |
| spelling | doaj.art-c9aef8cbfc3f432f809b3c835be244262023-11-23T12:27:12ZengMDPI AGNanomaterials2079-49912022-05-011210172110.3390/nano12101721Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel DiametersSeunghwan Lee0Jun-Sik Yoon1Junjong Lee2Jinsu Jeong3Hyeok Yun4Jaewan Lim5Sanguk Lee6Rock-Hyun Baek7The Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaThe Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaThe Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaThe Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaThe Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaThe Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaThe Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaThe Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Gyeongbuk, KoreaIn this study, threshold voltage (<i>V</i><sub>th</sub>) variability was investigated in silicon nanowire field-effect transistors (SNWFETs) with short gate-lengths of 15–22 nm and various channel diameters (<i>D</i><sub>NW</sub>) of 7, 9, and 12 nm. Linear slope and nonzero y-intercept were observed in a Pelgrom plot of the standard deviation of <i>V</i><sub>th</sub> (σ<i>V</i><sub>th</sub>), which originated from random and process variations. Interestingly, the slope and y-intercept differed for each <i>D</i><sub>NW</sub>, and σ<i>V</i><sub>th</sub> was the smallest at a median <i>D</i><sub>NW</sub> of 9 nm. To analyze the observed <i>D</i><sub>NW</sub> tendency of σ<i>V</i><sub>th</sub>, a novel modeling approach based on the error propagation law was proposed. The contribution of gate-metal work function, channel dopant concentration (<i>N</i><sub>ch</sub>), and <i>D</i><sub>NW</sub> variations (WFV, ∆<i>N</i><sub>ch</sub>, and ∆<i>D</i><sub>NW</sub>) to σ<i>V</i><sub>th</sub> were evaluated by directly fitting the developed model to measured σ<i>V</i><sub>th</sub>. As a result, WFV induced by metal gate granularity increased as channel area increases, and the slope of WFV in Pelgrom plot is similar to that of σ<i>V</i><sub>th</sub>. As <i>D</i><sub>NW</sub> decreased, SNWFETs became robust to ∆<i>N</i><sub>ch</sub> but vulnerable to ∆<i>D</i><sub>NW</sub>. Consequently, the contribution of ∆<i>D</i><sub>NW</sub>, WFV, and ∆<i>N</i><sub>ch</sub> is dominant at <i>D</i><sub>NW</sub> of 7 nm, 9 nm, and 12, respectively. The proposed model enables the quantifying of the contribution of various variation sources of <i>V</i><sub>th</sub> variation, and it is applicable to all SNWFETs with various <i>L</i><sub>G</sub> and <i>D</i><sub>NW</sub>.https://www.mdpi.com/2079-4991/12/10/1721variability modelingthreshold voltageSNWFETultrashort gate-lengthPelgrom’s lawnanowire diameter |
| spellingShingle | Seunghwan Lee Jun-Sik Yoon Junjong Lee Jinsu Jeong Hyeok Yun Jaewan Lim Sanguk Lee Rock-Hyun Baek Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters Nanomaterials variability modeling threshold voltage SNWFET ultrashort gate-length Pelgrom’s law nanowire diameter |
| title | Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters |
| title_full | Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters |
| title_fullStr | Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters |
| title_full_unstemmed | Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters |
| title_short | Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters |
| title_sort | novel modeling approach to analyze threshold voltage variability in short gate length 15 22 nm nanowire fets with various channel diameters |
| topic | variability modeling threshold voltage SNWFET ultrashort gate-length Pelgrom’s law nanowire diameter |
| url | https://www.mdpi.com/2079-4991/12/10/1721 |
| work_keys_str_mv | AT seunghwanlee novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters AT junsikyoon novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters AT junjonglee novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters AT jinsujeong novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters AT hyeokyun novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters AT jaewanlim novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters AT sanguklee novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters AT rockhyunbaek novelmodelingapproachtoanalyzethresholdvoltagevariabilityinshortgatelength1522nmnanowirefetswithvariouschanneldiameters |