6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-1 Lecture 9 - MOSFET (I) MOSFET I-V Characteristics October 6, 25 Contents: 1. MOSFET: cross-section, layout, symbols 2. Qualitative operation 3. I-V characteristics Reading assignment: Howe and Sodini, Ch. 4, 4.1-4.3 Announcements: Quiz 1: 1/13, 7:3-9:3 PM, (lectures #1-9); open book; must have calculator.
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-2 Key questions How can carrier inversion be exploited to make a transistor? How does a MOSFET work? How does one construct a simple first-order model for the current-voltage characteristics of a MOSFET?
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-3 1. MOSFET: layout, cross-section, symbols body source polysilicon gate drain gate n + p + n + n + p n inversion layer channel gate length gate oxide n p + p n + n + n + gate width n + STI edge Key elements: inversion layer under gate (depending on gate voltage) heavily-doped regions reach underneath gate inversion layer electrically connects source and drain 4-terminal device: body voltage important
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-4 Image removed due to copyright restrictions.
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-5 2 Circuit symbols Two complementary devices: n-channel device (n-mosfet) on p-si substrate (uses electron inversion layer) p-channel device (p-mosfet) on n-si substrate (uses hole inversion layer) I Dn D I D + Dn + S + S > VSB G G B B + + G B G V GS V BS V SD > S S I Dp D I Dp V SG D B (a) n-channel MOSFET (b) p-channel MOSFET
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-6 2. Qualitative operation Water analogy of MOSFET: Source: water reservoir Drain: water reservoir Gate: gate between source and drain reservoirs V GS G ID S inversion layer depletion region D VGS VDS water p B source gate drain Want to understand MOSFET operation as a function of: gate-to-source voltage (gate height over source water level) drain-to-source voltage (water level difference between reservoirs) Initially consider source tied up to body (substrate or back).
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-7 Three regimes of operation: 2 Cut-off regime: MOSFET: V GS <V T, V GD <V T with >. Water analogy: gate closed; no water can flow regardless of relative height of source and drain reservoirs. V GS <V T G V GD <V T S D p no inversion layer anywhere depletion region no water flow I D =
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-8 Linear or Triode regime: MOSFET: V GS >V T, V GD >V T, with >. Water analogy: gate open but small difference in height between source and drain; water flows. V GS >V T G V GD >V T S D p inversion layer everywhere depletion region Electrons drift from source to drain electrical current! V GS Q n I D E y I D ID small VDS ID small VDS VGS>VT VDS VDS VT VGS
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-9 Saturation regime: MOSFET: V GS >V T, V GD <V T ( > ). Water analogy: gate open; water flows from source to drain, but free-drop on drain side total flow independent of relative reservoir height! V GS >V T G V GD <V T S D p depletion region inversion layer "pinched-off" at drain side I D independent of : I D = I Dsat ID V GDsat =V T linear saturation sat =V GS -V T VDS
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-1 3. I-V characteristics Geometry of problem: L y V GS -t ox x j V BS = S I S inversion layer G depletion region D I D p B x 2 General expression of channel current Current can only flow in y-direction: I y = WQ n (y)v y (y) Drain terminal current is equal to minus channel current: I D = WQ n (y)v y (y)
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-11 I D = WQ n (y)v y (y) Rewrite in terms of voltage at channel location y, V c (y): If electric field is not too big: dv c (y) v y (y) µ n E y (y) = µ n dy For Q n (y) use charge-control relation at location y: Q n (y) = C ox [ V GS V c (y) V T ] for V GS V c (y) V T. All together: dv c (y) I D = Wµ n C ox (V GS V c (y) V T ) dy Simple linear first-order differential equation with one unknown, the channel voltage V c (y).
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-12 Solve by separating variables: I D dy = Wµ n C ox (V GS V c V T )dv c Integrate along the channel in the linear regime: -for y =, () = V c -for y = L, V c (L) = (linear regime) Then: L I D dy = Wµ n C ox (V GS V c V T )dv c or: W I D = µ n C ox (V GS V T ) L 2
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-13 For small : I D W µ n C ox (V GS V T ) L Key dependencies: I D (higher lateral electric field) V GS I D (higher electron concentration) L I D (lower lateral electric field) W I D (wider conduction channel) ID small VDS ID small VDS VGS>VT VDS VDS VT VGS This is the linear or triode regime.
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-14 In general, W I D = µ n C ox (V GS V T ) L 2 Equation valid if V GS V c (y) V T at every y. Worst point is y = L, where V c (y) =, hence, equation valid if V GS V T, or: V GS V T ID VDS=VGS-VT VGS VGS=VT VDS term responsible for bend over of I D : 2
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-15 To understand why I D bends over, must understand first channel debiasing: Q n (y) = C ox (V GS -V T ) E y (y) L > y > = L V c (y) y > V GS -V c (y) = L y V GS = local gate overdrive > V T L y Along channel from source to drain: y V c (y) Q n (y) E y (y) Local channel overdrive reduced closer to drain.
V T L y 6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-16 Impact of : Q n (y) = C ox (V GS -V T ) E y (y) L y = L y V c (y) L y VDS= V GS -V c (y) V GS = local gate overdrive As, channel debiasing more prominent I D rises more slowly with
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-17 3µm n-channel MOSFET Output characteristics (V GS = 4 V, V GS =.5 V ):
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-18 Zoom close to origin (V GS = 2 V, V GS =.25 V ):
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-19 Transfer characteristics ( = 1 mv, = 2 mv ):
6.12 - Microelectronic Devices and Circuits - Fall 25 Lecture 9-2 Key conclusions The MOSFET is a field-effect transistor: the amount of charge in the inversion layer is controlled by the field-effect action of the gate the charge in the inversion layer is mobile conduction possible between source and drain In the linear regime: V GS I D : more electrons in the channel I D : stronger field pulling electrons out of the source Channel debiasing: inversion layer thins down from source to drain current saturation as approaches: sat = V GS V T