ve6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-1 Lecture 10 - MOSFET (II) MOSFET I-V Characteristics (cont.) October 13, 2005 Contents: 1. The saturation regime 2. Backgate characteristics Reading assignment: Howe and Sodini, Ch. 4, §4.4 Announcements: Quiz 1: 10/13, 7:30-9:30 PM, (lectures #1-9); open book; must ha calculator. musthave calculator.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-2 Key questions • How does the MOSFET work in saturation? • Does the pinch-off point represent a block to current flow? • How come the MOSFET current still increases a bit with VDS in saturation? • How does the application of a back bias affect the MOSFET I-V characteristics?6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-3 1. The saturation regime Geometry of problem: n+ n+ n+ p S G D B 0 L depletion regionVBS=0 VGS VDS ID IS inversion layer y -tox 0 xj x Regimes of operation so far (VBS = 0): • Cut-off: VGS <VT , VGD <VT : no inversion layer anywhere underneath gate ID =0 • Linear: VGS >VT , VGD >VT (with VDS > 0): inversion layer everywhere underneath gate W VDSID = µnCox(VGS − − VT )VDSL 26.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-4 Output characteristics: ID 0 VGS VGS=VT VDS=VGS-VT 0 VDS6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-5 2 Review of Qn, Ey, Vc, and VGS − Vc(y) in linear regime as VDS increases: |Qn(y)| 0 |Ey(y)| 0 Vc(y) VDS 0 VGS-Vc(y) VGS VT VDS VDS=0 0 0 0 yL L L y y VDS 0 L y Cox(VGS-VT) local gate overdrive VDS=0 VDS=0 VDS=0VDS VDS VDS Ohmic drop along channel debiases inversion layer ⇒ ID rises more slowly with VDS6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-6 2 Drain current saturation As VDS approaches: VDSsat = VGS − VT increase in |Ey| compensated by decrease in |Qn|⇒ ID saturates to: IDsat = IDlin(VDS = VDSsat = VGS − VT ) Then: W IDsat = µnCox(VGS − VT )2 2LID VGS VGS=VT VDSsat=VGS-VT 0 linear saturation 0 cutoff VDS6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-7 W IDsat = µnCox(VGS − VT )2 2LTransfer characteristics in saturation: ID VDS>VDSsat=VGS-VT 0 0 VT VGS6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-8 2 What happens when VDS = VGS − VT ? Charge control relation at drain-end of channel: Qn(L)= −Cox(VGS − VDS − VT )=0 No inversion layer at end of channel??!! ⇒ Pinch-offPinch-offAt pinch-off: • charge control equation inaccurate around VT • electron concentration small but not zero • electrons move fast because electric field is very high • dominant electrostatic feature: acceptor charge • there is no barrier to electron flow (on the contrary!) inversion layer p DG +++++++++++ ----------------n+ drain depletion regions Ly��6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-9 2 Key dependencies of IDsat • IDsat ∝ (VGS − VT )2 Voltage at pinch-off point (Vc = 0 at source): p D G + ++++++++++ ----------------n+ Vc(L)=VDSsat=VGS-VT Drain current at pinch-off: ∝ lateral electric field ∝ VDSsat = VGS − VT ∝ electron concentration ∝ VGS − VT ⇒ IDsat ∝ (VGS − VT )2 • I ∝ 1 LDsat L ↓→ |Ey|↑6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-10 3µm n-channel MOSFET Output characteristics (VGS =0 − 4 V, ∆VGS =0.5 V ):6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-11 Transfer characteristics in saturation (VDS =3 V ):mo6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-12 2 What happens if VDS >VGS − VT ? Depletion region separating pinch-off point and drain widens (just like in reverse-biased pn junction) p D G +++++++++++ ----------------n+ Vc(L-∆L)=VDSsat=VGS-VT LL-∆L y To first order, ID does not increase past pinchoff: W ID = IDsat = µnCox(VGS − VT )2 2LTo second order, electrical channel length affected (”channel-length dulation”): VDS ↑⇒ Lchannel ↓⇒”channel-length modulation” ID ↑ 1 1 ∆L ID ∝ (1 + )L − ∆L L L6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-13 Experimental finding: ∆L ∝ VDS − VDSsat Hence: ∆L = λ(VDS − VDSsat)L Improved model in saturation: W IDsat = µnCox(VGS − VT )2[1 + λ(VDS − VDSsat)]2L ID VGS VGS=Vth VDSsat 0 0 VDS Also, experimental finding: 1 λ ∝ L6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-14 2. Backgate characteristics There is a fourth terminal in a MOSFET: the body. What does the body do? VDS depletion region inversion layer n+ p n+ VBS VGS>VT DG S B 0 L y ID Body contact allows application of bias to body with re -spect to inversion layer, VBS . Only interested in VBS < 0 (pn diode in reverse bias). Interested in effect on inversion layer ⇒ examine for VGS >VT (keep VGS constant).6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-15 Application of VBS < 0 increases potential build-up across semiconductor: −2φp ⇒−2φp − VBS Depletion region must widen to produce required extra field: ρ x 0 0 -qNa 0 E Eox Es -tox Qn xdmax(VBS) VBS=0 VBS<0 x -tox 0 xdmax(VBS) x φ 0 0 -tox VGS+φB VBS -φp Vox VB=-2φp VB=-2φp-VBSVVversion la er c is6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-16 Consequences of application of VBS < 0: • −2φp ⇒−2φp − VBS •|QB|↑⇒xdmax ↑ • since VGS constant, Vox unchanged ⇒ Eox unchanged ⇒ |Qs| = |QG| unchanged •|Qsy harge reduced!version layer harge is reduced!| = |Qn|+ |QB| unchanged, but |QB|↑⇒ |Qn|↓⇒ ininApplication of VBS < 0 with constant VGS reduces elec-tron concentration in inversion layer ⇒ VT ↑VT↑� � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-17 How does VT change with VBS ? In VT formula change −2φp to −2φp − VBS : VTGB (VBS )= VFB − 2φp − VBS + γ (−2φp − VBS ) In MOSFETs, interested in VT between gate and source: VGB = VGS − VBS ⇒ VTGB = VTGS − VBS Then: V GS = V GB T T + VBS And: V GS (VBS )= VFB − 2φp + γ (−2φp − VBS ) ≡ VT (VBS )T In the context of the MOSFET, VT is always defined in terms of gate-to-source voltage.� � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 10-18 Define: VTo = VT (VBS =0) Then: VT (VBS )= VTo + γ( −2φp − VBS − −2φp) ID VBS 0 cut-off saturation 0 VT VGS6.012 - Microelectronic
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