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Lecture #36 OUTLINE The MOSFET: • Qualitative theory • Long-channel I-V (“Square-Law” Theory) Reading: Textbook Chapter 17.2, 18.3.4 Spring 2007 EE130 Lecture 36, Slide 1 Qualitative Theory of the NMOSFET VGS < VT: depletion layer The potential barrier to electron flow from the source into the channel is lowered by applying VGS> VT VGS > VT : Electrons flow from the source to the drain by drift, when VDS>0. (IDS > 0.) VDS 0 VDS > 0 V I DS WQinvv WQ inv eff WQ inv eff DS L Spring 2007 EE130 Lecture 36, Slide 2 The channel potential varies from VS at the source end to VD at the drain end. (The inversion layer can be modeled as a resistor.) VGS > VT : VDS = VGS-VT VDS > VGS-VT 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 “pinched off” As VD is increased above VG-VT, the length DL of the “pinch-off” 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 VDsa t If DL is significant compared to L, then IDS will increase slightly with increasing VDS>VDsat, due to “channel-length modulation” Spring 2007 EE130 Lecture 36, Slide 3 Ideal MOSFET I-V Characteristics (Enhancement Mode NMOS Transistor) Saturation region Linear region Spring 2007 EE130 Lecture 36, Slide 4 Impact of Inversion-Layer Bias • When a MOS device is biased into inversion, a pn junction exists between the surface and the bulk. • If the inversion layer contacts a heavily doped region of the same type, it is possible to apply a bias to this pn junction. N+ poly-Si • VG is biased so that surface is inverted + + + + + + + + SiO2 N+ - - - - - - - - - p-type Si Spring 2007 • n-type inversion layer is contacted by N+ region • If a bias VC is applied to the channel, A reverse bias (VB-VC) is applied between the channel & body EE130 Lecture 36, Slide 5 Effect of VCB on fS, W, and VT • Application of a reverse body bias non-equilibrium – 2 Fermi levels (one for n-region, one for p-region) • separation = qVBC fS is increased by VCB • Reverse body bias widens W, increases Qdep Qinv decreases with increasing VCB, for a given VGB Spring 2007 2qN A Si (2fF VCB ) VT VFB VCB 2fF Cox EE130 Lecture 36, Slide 6 NMOSFET I-V Characteristics • VD > VS • Current in the channel flows by drift • Channel voltage VC(y) varies continuously between the source and the drain 2qN A Si (2fF VCB ( y)) VT VFB VCB ( y) 2fF Cox • Channel inversion charge density Qdep ( y) Qinv ( y) Coxe VG VFB VCB ( y) 2fS C oxe W Spring 2007 EE130 Lecture 36, Slide 7 1st-Order Approximation • If we neglect the variation of Qdep with y, then Qdep 2qN A Si (2f F VSB ) Qinv Coxe VG VT VSB VCB Qinv Coxe VG VT VS VC where VT = threshold voltage at the source end: 2qN A Si (2fF VSB ) VT VFB VSB 2fF Cox Spring 2007 EE130 Lecture 36, Slide 8 NMOSFET Current (1st-order approx.) • Consider an incremental length dy in the channel. The voltage drop across this region is dVC I DS dR I DS L 0 dy WTinv I DS I DS dy dy q eff nWTinv Qinv eff W VD I DS dy eff WQinv (VC )dVC VS VD W I DS eff Qinv (VC )dVC VS L VDS W I DS eff Coxe VG VT VDS in the linear region L 2 W I DS I Dsat Coxe eff (VG VT ) 2 in the saturation region 2L Spring 2007 EE130 Lecture 36, Slide 9 Saturation Current, IDsat • saturation region: VD VDsat VG VT I Dsat W Coxe eff (VG VT ) 2 2L 2qN A Si (2fF VSB ) VT VFB VSB 2fF Cox Spring 2007 EE130 Lecture 36, Slide 10