MIT 6 720J - Metal-Oxide-Semiconductor Field-Effect Transistor

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6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-1 Lecture 25 - The ”Long” Metal-Oxide-Semiconductor Field-Effect Transistor April 9, 2007 Contents: 1. Qualitative operation of the ideal MOSFET 2. Inversion layer transport 3. I-V characteristics of ideal MOSFET Reading assignment: del Alamo, Ch. 9, §§9.2-9.4 (9.4.1, 9.4.2) Announcements: Quiz 2: April 10, 7:30-9:30 PM; lectures #12-23. Open book. Calculator required. 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-2 Key questions • How does l a teral transport through the inversion layer take place? • What are the most important regimes of operation of a MOS-FET? • What are the key functional dependencies of the MOSFET d rain current on the g a te and drain voltage? • Why under some conditions does the drain current saturate? 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-3 1. Qualitative operation of the ideal M OSFET Water analogy of MOSFET: • Source: water reservoir • Drain: water reservoi r • Gate: gate between source and drain reservoirs n+ n+ n+ p VGS VDS source draingate water Want to understand MOSFET operation as a f unction of : • gate-to-source voltage (gate height over source water level) • drain-to-source voltage (water level difference between reservoirs) Initially consider s ource tied up to body (substrate or back). 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-4 Three regimes of operation: � Cut-off regi me: • MOSFET: VGS < VT, VGD < VT with VDS > 0 . • Water analogy: gate closed; no water can flow regardless of relative height of source and drain reservoirs. cut-off ID = 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-5 � Linear or Triode regime: • MOSFET: VGS > VT, VGD > VT, with VDS > 0 . • Water ana l o g y: gate open but small difference in height between source and drain; water flows. linear or triode Electrons d rift from source to drain ⇒ electrical current! • VGS ↑ → |Qi| ↑ → ID ↑ • VDS ↑ → Ey ↑ → ID ↑ ID IDsmall VDS small VDS VGS>VT VDS 0 0 0 VDS VT VGS 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-6 � Saturation regime: • MOSFET: VGS > VT, VGD < VT (VDS > 0 ). • Water ana l o g y: gate open; water flows from source to drain, but free-drop on drain side ⇒ total flow independent of relative reservo i r height! saturation ID independent of VDS: ID = IDsat VGDsat=VT ID saturation linear 0 VDSsat=VGS-VT VDS 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-7 2. Inversion layer transport Want a formalism to describe lateral current along inversion layer. n+ n+ n+ p S G D B y 0 0 L inversion� layer depletion� region VBS VGS VDS ID IS x -xox xj Not interested in details of electron distribution in depth (along x). Define s heet car rier concentration: ns(y) = �∞ n(x, y)dx [cm −2]0 General expression fo r inversion layer current: Ie � −qW vey(y)ns(y) Note: Ie independent of y. 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-8 Define s heet charge density of inversion layer: Qi(y) = −qns(y) [C/cm2] Rewrite current equation: Ie � W vey(y)Qi(y) We have just performed the sheet charge approximation (SCA). • it is physically meaningful to define an average lateral velocity for all electrons in inversion layer • SCA suitable if distribution of vey in depth does not change too rapidly in the scale of the changes that are taking pl a ce in n Assu me now mobility-limited electron drift (low lateral fi eld ) [we will und o this for the short MOSFET]: vey(y) � −µeEy(y) Then: Ie � −W µeEy(y)Qi(y) 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/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 25-9 Ie � −W µeEy(y)Qi(y) Rewrite this in terms of V (y), the voltage along the inversion layer. Definition of V (y): V (y) = φs(y) − φs(y = 0 ) The source (located at y = 0) is reference for V . Then, l a teral electric field along inversion layer is: dV (y)Ey(y) = − |ydy Insert this in current equation: dV (y)Ie = W µeQi(y) |ydy Now need to relate Qi(y) with V (y). 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/3.43J


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