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Institute of Solid State PhysicsTechnische Universität Graz11. MOSFETsDec. 12, 2018
Gradual channel lampx.tugraz.at/ hadley/psd/L10/gradualchannelapprox.php
Gradual channel approximationOhm's lawj nevd ne n E yI Ztj Ztne n E y Ze n ns E yns nt is the sheet charge at the interface.Q Cox VG Vch ( y ) VT ns ( y ) ee
Gradual channel approximationI Ztj Ztnevd Zens n E ydifferential equation for Vchhttp://lampx.tugraz.at/ hadley/psd/L10/gradualchannelapprox.php
Gradual channel approximation
MOSFET Gradual Channel Approximationhttp://lampx.tugraz.at/ hadley/psd/L10/gradualchannelapprox.php
Gradual channel approximationValid in the linear regime (until pinch-off occurs at the drain).
MOSFET-saturation voltage VD2 ZI nCox VG VT VD L2 At pinch-off, dIds/dVds 0dIZ nCox VG VT VD 0dVD LVsat VG VT A MOSFET in saturation is a voltage controlled current source.
MOSFET - saturation currentUse the saturation voltage atpinch-off to determine thesaturation currentVsat VG VT VD2 ZI nCox VG VT VD L2 I satZ2 nCox VG VT 2L
MOSFET (saturation regime)I sat Z2 nCox VGS VT 2LIDcut-off
MOSFET (linear regime)Channel conductance in thelinear regime. For small VDZI nCox VG VT VD LdI D ZgD nCox VG VT dVD LTransconductancedI D Zgm nCoxVDdVG L
MOSFET (saturation regime)I satZ2 nCox VG VT 2LTransconductancedI D Zgm nCox VG VT dVG LA MOSFET in the saturation regime acts like a voltage controlled current source.
SaturationGGDSPotentialDElectric field strengthAlexander Schiffmann, Master Thesis (2016)
MOSFET (saturation regime)I sat Z2 nCox VG VT 1 VD Vsat 2LExperimentally: channel length modulation1 L
High frequenciesi out g m v Gi in 2 fCG v Gi in i outf gm1 2 fT2 CG sFor large E, Ohm's law (j ne E) is notvalid. The electron velocity saturates. Forvelocity saturation:fT vsL
Constant E-field ScalingGate length L, transistor width Z, oxide thickness tox are scaled down.Vds, Vgs, and VT are reduced to keep the electric field constant.Power density remains constant.L 45 tox1975 - 1990: "Days of happy scaling"
Constant E-field scalingI sat L sL, Z2 n ox VG VT tox2LZ sZ ,I sat sI satgm dI D Z n ox VG VT dVG Ltoxtox stox ,Vth sVthIsat gets smallerTransconductance stays the same.Power per transistor decreases like L2. Power per unit arearemains constant.
The heat dissipation problemMicroprocessors are hot 100 CHotter operation will cause dopants to diffuseWhen more transistors are put on a chip they mustdissipate less power.Power per transistor decreases like L2.
Jan 1 1970Transistor count doubles about every 2 yearshttps://en.wikipedia.org/wiki/Transistor count
Tensile silicon nitride film over the NMOS and a compressive siliconnitride film over the PMOS improves the lay/athlon64-venice 2.htmlDual stress liners
Gate dielectricThinner than 1 nm:electrons tunnelLarge dielectricconstant desirable r(SiO2) 4 r(Si3N4) 7
www.iwailab.ep.titech.ac.jp
High-k as/gate-oxide-studies/
Short channel effectsSOI: silicon on insulator
CMOS SOIFransila
Intel Pentium 490 nmIntel Pentium D65 nmIntel Core 2 Duo45 nmIntel Atom Z6xx Series 45 nmIntel Core 2 Celeron45 nmIntel Core i7-90032 nmIntel Xeon 5600 Series 32 nmIntel Ivy bridge tri-gate22 nmIntel Haswell FinFET16 nm
Intel 22nm 3D tri-gate 22nm/gallery/images/Intel-22nm Transistor.jpg
FinFEThttps://www.youtube.com/watch?v Jctk0DI7YP8
FinFET, Tri-gateDrain induced barrier loweringRobert Chau, Intel
Subthreshold currentFor VG VT the transistor should switch off but there is a diffusion current. Thecurrent is not really off until 0.5 V below the threshold voltage.Weak inversion e VG VT I D exp kTB Subthreshold swing: 70-100 mV/decade
2 2 ox sat n G T ox Z IVV Lt Power per transistor decreases like L2. Power per unit area remains constant. LsL Z sZ t st V sV , , , ox ox th th IsI sat sat Transconductance stays the same. I sat gets smaller
