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Massachusetts Institute of Technology
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6.720J | Integrated Microelectronic Devices
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2024
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19
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lacieabellaot

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 frequency, 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/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 27-2 Key questions • What are the capacitances associated with the inversion layer charge? • What is the topology of a small-signal equivalent circuit model for the MOSFET? • What are the key bias and geometry dependencies of all smallsignal 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/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 27-3 1. Charge-voltage characteristics of ideal MOSFET (cont.) � Inversion charge: VDS VGS G n+ S D n+ n+ VBS inversion� layer depletion� region LS p LD B For VGS > VT : QI = W � L 0 Qi(y)dy Change variables to V : QI = W � V DS 0 Qi(V ) dy dV 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/3.43J - Integrated Microelectronic Devices - Spring 2007 QI = W � V DS 0 Qi(V ) Lecture 27-4 dy dV dV From channel current equation, we have: dy W µe |V = − Qi (V ) dV ID Then: W 2µe � VDS 2 QI = − Qi (V )dV ID 0 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/3.43J - Integrated Microelectronic 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) VGS>VT VDS=VDSsat=VGS-VT - 2 WLCox(VGS-VT) 3 0 0 VDSsat VDS Used fundamental charge control relationship ⇒ expression only 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/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 27-6 For saturation: set VDS = VDSsat = VGS − VT in linear regime expression and get: 2 QI = − W LCox (VGS − VT ) 3 QI -WLCox(VGS-VT) VDS=VDSsat=VGS-VT VGS>VT - 2 WLCox(VGS-VT) 3 VGSVT WLCox Cgsi 2 WLC ox 3 1 WLC ox 2 Cgdi 0 0 VDSsat VDS • Linear regime (small VDS ): uniform inversion layer charge: n+ n+ n+ Cgsi � Cgdi � 12 W LCox p • Saturation regime (VDS > VDSsat ): channel pinched-oﬀ: n+ n+ n+ Cgs � 23 W LCox Cgd � 0 p 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 Microelectronic 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 bias: MOSFET� small-signal� equivalent� circuit model i�D=ID+id + v - ds + v - bs VBS vgs + - VGS VDS I�D i�d = VDS VGS VBS + vgs + + v - ds + v - bs Key points: • Small signal is small ⇒ non-linear device behavior becomes lin ear. • Can separate response of MOSFET to bias and small signal. • Since response is linear, superposition applies ⇒ eﬀects of dif ferent small-signals 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) 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 Microelectronic Devices - Spring 2007 Lecture 27-10 id linear on small-signal drives: id � gmvgs + gdvds + gmbvbs Deﬁne: gm ≡ transconductance [S] gd ≡ output or drain conductance [S] gmb ≡ back transconductance [S] Equivalent circuit model representation: D gmvgs G go B gmbvbs S Approach to computing gm, gd, and gmb: gm � ∂ID | ∂VGS VDS ,VBS gd � ∂ID | ∂VDS VGS ,VBS gmb � ∂ID | ∂VBS VGS ,VDS Will deal with gmb after we have dealt with body eﬀect. 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 Microelectronic Devices - Spring 2007 Lecture 27-11 � Transconductance, gm: gm � ∂ID | ∂VGS VDS ,VBS • Linear regime: ID = W 1 µe Cox (VGS − Vth − VDS )VDS L 2 W µe Cox VDS L gm = • Saturation regime: IDsat = gm = W µe Cox (VGS − Vth)2 2L � � � � � W W µe Cox (VGS − Vth) = 2 µn Cox ID L L gm gm gm saturation saturation saturation linear VGS cut-off 0 0 VDSsat linear VDS VDS cut-off cut-off 0 VDS linear 0 0 VT VGS 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]. ID 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 27-12 � Output conductance, gd: gd � ∂ID | ∂VDS VGS ,VBS • Linear regime: ID = W 1 µe Cox (VGS − Vth − VDS )VDS L 2 gd = W µeCox (VGS − Vth − VDS ) L • Saturation regime: IDsat = W µe Cox (VGS − Vth)2 2L gd = 0 go go linear linear VGS 0 0 saturation VDSsat cut-off VDS VDS cut-off 0 0 VT saturation 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 Microelectronic Devices - Spring 2007 Lecture 27-13 � Add capacitors: D CjD Cgdi gmvgs G go B CjS Cgsi S CjB In saturation: Cgdi = 0, CjB = 0, go = 0 D CjD gmvgs G B CjS Cgsi S 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 Microelectronic Devices - Spring 2007 Lecture 27-14 3. Short-circuit current-gain cut-oﬀ frequency fT : ﬁgure of merit to evaluate the frequency response of transistors. fT provides insight into electron transport in MOSFET channel For fT , MOSFET biased with output shorted from the small-signal point of view: ID+id(t) ig(t) vgs(t) VGS VDS + - With MOSFET in saturation, fT deﬁned as frequency at which small signal current gain, h21 goes to unity. id |h21 (fT )| = | |vds=0 = 1 ig As f ↓ ⇒ h21 → ∞ . 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 Microelectronic Devices - Spring 2007 Lecture 27-15 � Computation of fT : small-signal equivalent circuit model: ig(t) G D id(t) + vgs(t) gmvgs Cgsi - S S ig and id given by: ig = jωCgsivgs id = gmvgs h21 given by: h21 = gm jωCgsi Magnitude of h21 is: |h21 | = gm ωCgsi 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 Microelectronic Devices - Spring 2007 Lecture 27-16 Evolution of h21 with frequency: log� |h21| 1 ωT log ω |h21 | becomes unity at: ωT = gm Cgsi or fT = gm 2πCgsi 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 Microelectronic Devices - Spring 2007 Lecture 27-17 � Bias dependence of fT : fT = 1 3 µe (VGS − VT ) 2π 2 L2 fT VDS>VDSsat=VGS-VT 0 0 VT VGS Key dependences: • fT increases linearly with VGS (gm linear in VGS ) • fT independent of VDS (gm, Cgsi independent of VDS ) • fT increases linearly with µe (gm linear in µe ) • fT scales as L−2 (gm scales as L−1, Cgsi scales as L) 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 Microelectronic Devices - Spring 2007 Lecture 27-18 � Physical meaning of fT fT has units of inverse time. • Deﬁne delay time: 1 2 L2 τd = = 2πfT 3 µe (VGS − VT ) Physical meaning of τd: Delay time is average time for an electron to cross the channel from source to drain. • Compute delay time directly. First, time it takes for electrons to travel distance dy drifting at velocity ve: dy dt = ve Then channel transit time is: τt = � L 0 dy ve (y) See Prob. 9.4 for a derivation of transit time: 2 L2 τt = = τd 3 µe (VGS − VT ) fT gives idea of intrinsic speed of 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/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 27-19 Key conclusions • In saturation, inversion charge results in: 2 Cgsi � W LCox and Cgdi = 0 3 • Transconductance. In saturation regime: √ g m ∝ ID • Drain conductance. In saturation regime: gd � 0 • fT : ﬁgure of merit to characterize frequency response of MOS FET • fT reﬂects intrinsic delay associated with electron transit from source to drain 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].

L27: I-V Characteristics (Cont.) - Body Effect, Back Bias

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