6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-1 Lecture 11 - MOSFET (III) MOSFET Equivalent Circuit Models October 18, 2005 Contents: 1. Low-frequency small-signal equivalent circuit model 2. High-frequency small-signal equivalent circuit model Reading assignment: Howe and Sodini, Ch. 4, §4.5-4.66.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-2 Key questions • What is the topology of a small-signal equivalent cir-cuit model of the MOSFET? • What are the key dependencies of the leading model elements in saturation?� � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-3 1. Low-frequency small-signal equivalent cir-cuit model Regimes of operation of MOSFET: VGS VBS VDS ID VDS ID VGS VGS=VT VDSsat=VGS-VT 0 0 linear saturation cutoff • Cut-off: ID =0 • Linear: W VDSID = µnCox(VGS − − VT )VDSL 2 • Saturation: W ID = IDsat = µnCox(VGS −VT )2[1+λ(VDS −VDSsat)]2LEffect of back bias: VT (VBS )= VTo + γ( −2φp − VBS − −2φp)6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-4 Small-signal device modeling In many applications, interested in response of device to a small-signal applied on top of bias: VGS VBS VDS ID+id vgs vbs vds + -++ --Key points: • Small-signal is small ⇒ response of non-linear components becomes linear • Can separate response of MOSFET to bias and small signal. • Since response is linear, superposition can be used ⇒ effects of different small signals are independent from each other6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-5 MOSFET small-signal VGS VBS VDS ID+id vgs vbs vds + -++ --VGS VBS VDS ID id vgs vbs vds + -++ --circuit model = + equivalent Mathematically: iD(VGS + vgs,VDS + vds,VBS + vbs) ∂ID ∂ID ∂IDID(VGS,VDS,VBS )+ Qvgs + ∂VDS Qvds + Qvbs∂VGS ∂VBS| | |where Q ≡ (VGS ,VDS,VBS )bias point Small-signal id: id gmvgs + govds + gmbvbs Define: gm ≡ transconductance [S] go ≡ output or drain conductance [S] gmb ≡ backgate transconductance [S] Then: ∂ID ∂ID ∂ID gm ∂VGS | go ∂VDS | gmb ∂VBS |Q Q Q� � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-6 2 Transconductance In saturation regime: W ID = µnCox(VGS − VT )2[1 + λ(VDS − VDSsat)]2LThen (neglecting channel length modulation): ∂ID W gm = | µnCox(VGS − VT )Q∂VGS L Rewrite in terms of ID: � W gm = �2 µnCoxIDL gmgm saturation saturation cut-off 0 0VTVGS0 ID 06.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-7 Transconductance of 3 µm nMOSFET (VDS =2 V ): Equivalent circuit model representation of gm: id G D+ vgs gmvgs -S B6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-8 2 Output conductance In saturation regime: W ID = µnCox(VGS − VT )2[1 + λ(VDS − VDSsat)]2LThen: ∂ID W go = ∂VDS | = µnCox(VGS − VT )2λ λID ∝ ID Q 2L L Output resistance is inverse of output conductance: 1 L ro = ∝ go ID go go saturationsaturation cut-off 0 0 VT VGS0 ID 06.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-9 Output conductance of 3 µm nMOSFET: Equivalent circuit model representation of go: id G D+ vgs ro -S B� � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-10 2 Backgate transconductance In saturation regime (neglect channel-length modulation): W ID µnCox(VGS − VT )2 2LThen: ∂ID W ∂VT gmb = ∂VBS | = µnCox(VGS − VT )(− ∂VBS | )Q QL Since: VT (VBS )= VTo + γ( −2φp − VBS − −2φp) Then: ∂VT −γ ∂VBS | = Q 2 −2φp − VBS All together: γgm gmb = 2 −2φp − VBS gmb inherits all dependencies of gm6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-11 Body of MOSFET is a true gate: output characteristics for different values of VBS (VBS =0 − (−3) V, ∆VBS = −0.5 V , VGS =2 V ): Equivalent circuit model representation of gmb: G S D+ -vgs gmbvbs -id vbs B+6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-12 Complete MOSFET small-signal equivalent circuit model for low frequency: G S D+ -vgs gmvgs gmbvbs ro -id vbs B+6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-13 2. High-frequency small-signal equivalent cir-cuit model Need to add capacitances. In saturation: source drain gateCfringe Cfringe CjCj Cgs,i Csb,i CovCov CjswCjsw n+ n+ n+ p body Cgs ≡ intrinsic gate capacitance + overlap capacitance, Cov (+fringe) Cgd ≡ overlap capacitance, Cov (+fringe) Cgb ≡ (only parasitic capacitance) Csb ≡ source junction depletion capacitance +sidewall (+channel-substrate capacitance) Cdb ≡ drain junction depletion capacitance +sidewall6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-14 Complete MOSFET high-frequency small-signal equiva-lent circuit model: idCgd G + -vgs Cgs Csb gmvgs gmbvbs ro + vbs -D S B Cdb Plan for development of capacitance model: • Start with Cgs,i – compute gate charge QG = −(QN + QB) – compute how QG changes with VGS • Add pn junction capacitances� � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-15 Inversion layer charge in saturation � L � QN (VGS )= W Qn(y)dy = W VGS −VT Qn(Vc) dy dVc00 dVc But: dVc ID = − dy WµnQn(Vc) Then: W 2Lµn VGS −VT Q2QN (VGS )= − n(Vc)dVcID 0 Remember: Qn(Vc)= −Cox(VGS − Vc − VT ) Then: QN (VGS )= − ox VGS −VTW 2LµnC2 (VGS − Vc − VT )2dVcID 06.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-16 Do integral, substitute ID in saturation and get: 2 3 WLCox(VGS − VT )QN (VGS )= − Gate charge: QG(VGS )= −QN (VGS ) − QB,max Intrinsic gate-to-source capacitance: C= dQG dVGS = 2 3 ox Cgs = 2 3 ox + WCov gs,i WLCMust add overlap capacitance: WLCGate-to-drain capacitance - only overlap capacitance: Cgd = WCov� � � � � � � � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 11-17 source gate body channel polysilicon gate p p n n p+ n+n+ n+ p+ n+ n+ n+n+ gate length STI edge drain gate oxide inversion layer gate width Body-to-source capacitance = source junction capacitance: � qsNaCsb = Cj +Cjsw = WLdif f � +(2Ldif f +W )CJSW 2(φB − VBS )Body-to-drain capacitance = drain junction capacitance: � qsNaCdb = Cj +Cjsw = WLdif f � +(2Ldif f +W )CJSW 2(φB − VBD)� � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005
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