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1. Lecture #25 вҖў Design Project: вҖ“ Due in class (5 PM) on Thursday May 1st вҖў 20 pt penalty for late submissions, accepted until 5 PM on 5/8 вҖ“ Your BJT design does not need to meet the performance specifications when WB and NB are varied by +/- 10% вҖ“ Equation for вҲҶEG assumes NE is in cm-3 and T is in K EE130 QUIZ SCORE TREND вҖў Quiz#5 Results: 30 (undergrad.вҖҷs only) 21.6 20.5 20 18.9 N=60 17.9 17.9 10 Mean=20.5 0 Std.Dev.=3.6 Q1 Q2 Q3 Q4 Q5 Spring 2003 EE130 Lecture 25, Slide 1 OUTLINE вҖў NMOSFET I-V вҖў Effective mobility вҖў Transconductance вҖў PMOSFET I-V вҖў Subthreshold current Spring 2003 EE130 Lecture 25, Slide 2 1

2. Ideal MOSFET I-V Characteristics (Enhancement Mode NMOS Transistor) Saturation Linear region region Spring 2003 EE130 Lecture 25, Slide 3 Review: Qualitative Operation of the NMOSFET depletion layer The potential barrier to electron flow from the source into the channel is lowered by applying VGS> VT Electrons flow from the source to the drain by drift, when VDS>0. (IDS > 0.) The channel potential varies from VS at the source end to VD at the drain end. (The inversion layer can be Spring 2003 EE130 Lecture 25, Slide 4 modeled as a resistor.) 2

3. When VD is increased to be equal to VG-VT, the inversion-layer charge density at the drain end of the channel equals zero, i.e. the channel becomes вҖңpinched offвҖқ As VD is increased above VG-VT, the length вҲҶL of the вҖңpinch-offвҖқ region increases. The voltage applied across the inversion layer is always VDsat=VGS-VT, and so the current saturates: I Dsat = I DS V DS =VDsat If вҲҶL is significant compared to L, then IDS will increase slightly with increasing VDS>VDsat, due to вҖңchannel-length modulationвҖқ Spring 2003 EE130 Lecture 25, Slide 5 NMOSFET I-V Characteristics вҖў VD > VS вҖў Current in the channel flows by drift вҖў Channel voltage VC(y) varies continuously between the source and the drain 2qN AОө Si ( 2ПҲ B + VCB ( y )) VT = VFB + VC ( y ) + 2ПҲ B + Cox вҖў Channel inversion charge пЈ® Q ( y) пЈ№ Qinv ( y ) = вҲ’Coxe пЈҜVG вҲ’ VFB вҲ’ VC ( y ) вҲ’ 2ПҲ B вҲ’ dep пЈ° Coxe пЈәпЈ» W Spring 2003 EE130 Lecture 25, Slide 6 3

4. 1st-Order Approximation вҖў Neglect variation of Qdep with y Qdep = 2qN AОө Si (2ПҲ B + VSB ) вҮ’ Qinv = вҲ’Coxe [VG вҲ’ VT + VS вҲ’ VC ] where VT = threshold voltage at the source end: 2qN AОө Si ( 2ПҲ B + VSB ) VT = VFB + VS + 2ПҲ B + Cox Spring 2003 EE130 Lecture 25, Slide 7 NMOSFET Current (1st-order approx.) вҖў Consider an incremental length dy in the channel. The voltage drop across this region is dy dy I dy dVC = I DS dR = I DS = I DS = вҲ’ DS ПғWTinv qВөeff nWTinv Qinv Вөeff W L VD вҲ«I 0 DS dy = вҲ’ вҲ« Вөeff WQinv (VC )dVC VS W VD I DS = вҲ’ Вөeff вҲ« Qinv (VC )dVC L VS W пЈ® V пЈ№ I DS = Вөeff Coxe пЈҜVGS вҲ’ VT вҲ’ DS пЈәVDS in the linear region L пЈ° 2 пЈ» W I DS = I Dsat = Coxe Вөeff (VGS вҲ’ VT ) 2 in the saturation region 2L Spring 2003 EE130 Lecture 25, Slide 8 4

5. Effective Mobility пЈ«V пЈ¶ I DS = WQinv v = WQ inv Вөeff E = WQ inv Вөeff пЈ¬ DS пЈ· пЈӯ L пЈё = (W / L) Вөeff Coxe (VG вҲ’ VT )VDS where Вөeff is the effective electron mobility The NMOSFET can be modelled as a resistor at low VDS: VDS L RDS = = I DS WВөeff Coxe (VG вҲ’ VT ) Spring 2003 EE130 Lecture 25, Slide 9 Вөeff vs. Effective Normal Field (Vgs + V t + 0.2)/6Toxe (MV/cm) (NFET) Scattering mechanisms: вҖў coulombic scattering вҖў phonon scattering вҖў surface roughness scattering (PFET) вҖ“(Vgs + 1.5V t вҖ“ 0.25)/6Tox e (MV/cm) Spring 2003 EE130 Lecture 25, Slide 10 5

6. The вҖңBody EffectвҖқ VT is a function of VSB: VT = VT 0 + 2qN AОө Si Coxe ( 2ПҲ B + VSB вҲ’ 2ПҲ B ) = VT 0 + Оі ( 2ПҲ B + VSB вҲ’ 2ПҲ B ) where Оі is the body effect parameter When the source-body pn junction is reverse-biased, |VT| increases. Usually, we want to minimize Оі so that IDsat вҲқ|VGS вҖ“ VT| will be the same for all transistors in a circuit Spring 2003 EE130 Lecture 25, Slide 11 Problem with the вҖңSquare Law TheoryвҖқ вҖў Assumes that gate charge is purely balanced by inversion charge вҖў Ignores variation in depletion width with distance y Spring 2003 EE130 Lecture 25, Slide 12 6

7. Modified Model W m I DS = Coxe Вөeff (VGS вҲ’ VT вҲ’ VDS )VDS L 2 Cdm 3T where m = 1 + = 1 + oxe since Оө Si = 3Оө Si O2 Coxe Wdm Spring 2003 EE130 Lecture 25, Slide 13 Modified Model: IDsat & Transconductance вҖў saturation region: V вҲ’ VT VD вүҘ VDsat = GS m W I Dsat = Coxe Вөeff (VGS вҲ’ VT )2 2mL вҖў transconductance: gm= dIDS/dVGS W g msat = Coxe Вө eff (VGS вҲ’ VT ) mL Spring 2003 EE130 Lecture 25, Slide 14 7

8. MOSFET VT Measurement вҖў VT can be determined by plotting IDS vs. VGS, using a low value of VDS Spring 2003 EE130 Lecture 25, Slide 15 P-Channel MOSFET вҖў The PMOSFET turns on when VGS < VTp вҖ“ Holes flow from SOURCE to DRAIN вҮ’ DRAIN is biased at a lower potential than the SOURCE VG вҖў VDS < 0 VS VD GATE IDS вҖў IDS < 0 P+ P+ вҖў |IDS| increases with N вҖў |VGS - VTp| вҖў |VDS| (linear region) VB вҖў In CMOS technology, the threshold voltages are usually symmetric: VTp = -VTn Spring 2003 EE130 Lecture 25, Slide 16 8

9. PMOSFET I-V VGS вҲ’ VTp вҖў Linear region: 0 < VDS < m W m I DS = вҲ’ Coxe Вө p ,eff (VGS + VTp вҲ’ VDS )VDS L 2 VGS вҲ’ VTp вҖў Saturation region: VDS > m W I DS = I Dsat = вҲ’ Coxe Вө p ,eff (VGS вҲ’ VTp ) 2 2mL m = 1 + (3Toxe/Wdm ) is the bulk-charge factor Spring 2003 EE130 Lecture 25, Slide 17 Sub-Threshold Leakage Current вҖў We had previously assumed that there is no channel current when VGS < VT. This is incorrect. вҖў Consider VS close to 2ПҲB: There is some inversion charge at the surface, which gives rise to subthreshold current flowing between the source and drain: 2 W пЈ« kT пЈ¶ q (VG вҲ’VT ) / mkT I DS = Вөeff Coxe ( m вҲ’ 1)пЈ¬пЈ¬ пЈ·пЈ· e (1 вҲ’ e вҲ’ qVDS / kT ) L пЈӯ q пЈё Spring 2003 EE130 Lecture 25, Slide 18 9

10. Sub-Threshold Slope S вҲ’1 пЈ« d (log10 I DS ) пЈ¶ S вүЎ пЈ¬пЈ¬ пЈ·пЈ· пЈӯ dV GS пЈё kT C = ln(10)(1 + dm ) q Coxe Spring 2003 EE130 Lecture 25, Slide 19 VT Design Tradeoff Spring 2003 EE130 Lecture 25, Slide 20 10

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