6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 27-1 Lecture 27 - The ”Long” Metal-Oxide-Semiconductor Field-Effect Transistor (cont.) April 13, 2007 Contents: 1. Charge-voltage characteristics of ideal MOSFET (cont.) 2. Small-signal behavior of ideal MOSFET 3. Short-citcuit current-gain cut-off f requency, fT Reading assignment: del Alamo, Ch. 9, §§9.5 (9.5.2), 9.6 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-2 Key q uestions • What are the capacitances associated wi th the inversion layer charge? • What is the topology of a small-sig nal equivalent circuit mod el for the MOSFET? • What are the key bias and geometry dependencies of all small-signal elements in the model? • How does one characterize the frequency response of a transistor? Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-3 1. Charge-voltage characteristics of ideal MOSFET (cont.) � Inversion charge: VDS n+ n+ n+ p S G D B inversion� layer depletion� region VGS LS LD VBS For VGS > VT: � L QI = W Qi(y)dy 0 Change variables to V : � VDS dy QI = W Qi(V ) dV 0 dV Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].� � 6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-4 VDS dy QI = W Qi(V ) dV 0 dV From channel current equation, we have: dy W µe dV |V = − ID Qi(V ) Then: QI = − WI2D µe 0 VDS Qi2(V )dV Now use charge-control relationship: Qi(V ) = −Cox(VGS − V −VT) Finally get: 2 (VGS − VT)2 + (VGS −VT)(VGD −VT) + (VGD − VT)2 QI = W LCox −3 (VGS − VT) + (VGD − VT) Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-5 2 (VGS − VT)2 + (VGS −VT)(VGD −VT) + (VGD − VT)2 QI = W LCox −3 (VGS − VT) + (VGD − VT) Evolution of QI with VDS: QI -WLCox(VGS-VT) VDS=VDSsat=VGS-VT VGS>VT 2 WLCox(VGS-VT)3 0 0 VDSVDSsat -Used fundamental charge control relationship expression o nly ⇒valid in linear regime. For small VDS: QI � −W LCox(VGS − VT) Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-6 For saturation: set VDS = VDSsat = VGS − VT in linear regime expression and g et: 2 QI = −3 W LCox(VGS − VT) QI -WLCox(VGS-VT) VDS=VDSsat=VGS-VT VGS>VT 2 -WLCox(VGS-VT)3 VGS<VT 0 0 VDSVDSsat Reduction of QItowards saturation is another manifestation of | |channel debia sing: |Qi(y)| VDS=0 Cox(VGS-VT) VDS=VDSsat 0 0 y ΔL Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-7 � Capacitance associated with i nversion charge: Inversion charge supplied by source and drain need two capacitors ⇒23 VDS 12 VDS)2 ∂QIVGD =1 W LCoxVGS − VT −Cgsi (VGS − VT) = −∂VGS|2 (VGS −VT − 13 VDS 12 VDS)2 ∂QIVGS =1 W LCoxVGS −VT −Cgdi (VGS −VDS − VT) = −∂VGD|2 (VGS − VT − Expressions valid i n l i near regime. Note that fo r small VDS: 1 Cgsi � Cgdi � W LCox 2 For saturation regime, set VDS = VDSsat = VGS −VT and get: 2 Cgsi = W LCox 3 Cgdi = 0 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-8 Evolution of Cgsi and Cgdi with VDS: WLCox 1 WLCox 2 Cgsi Cgdi VDS VGS>VT C WLCox 2 VDSsat 3 0 0 • Linear regime (small VDS): uniform inversion layer charge: p n+ n+ n+ Cgsi � Cgdi � 12 W LCox • Saturation regime (VDS > VDSsat): channel pinched-off: p n+ n+ n+ Cgs � 23 W LCox Cgd � 0 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-9 2. Small-signal behavior of ideal MOSFET In many applications, interested in response of device to small signal applied on top of bi a s: MOSFET� small-signal� equivalent� circuit model i�D=ID+id I�D i�d + vds -= VDS VDS+ ++ ++ vvgs -vbs gs -vbs--VGS VGSVBS VBS Key points: Small signa l is small non-linear device behavior becomes lin-• ⇒ear. • Can separate response of MOSFET to bias an d small si g nal. Since response is linear, s uperposition applies effects of dif-• ⇒ferent small-signal s independent from each other. Mathematically: iD(VGS, VDS, VBS; vgs, vds, vbs) � ID(VGS, VDS, VBS) + id(vgs, vds, vbs) and id(vgs, vds, vbs) = id(vgs) + id(vds) + id(vbs) + vds -Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 27-10 id linear on s mall-signal drives: id � gmvgs + gdvds + gmbvbs Define: gm ≡ transconductance [S] gd ≡ output or