L37: BJT C-V Characteristics, Small-Signal Equivalent Circuit Models

6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 37-1 Lecture 37 - Bipolar Junction Transistor (cont.) May 7, 2007 Contents: 1. Common-emitter short-circuit current-gain cut-off fre­ quency, fT Reading material: del Alamo, Ch. 11, §11.4.2 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 37-2 Key questions • How is the frequency response of a transistor assessed? • What determines the frequency response of an ideal BJT? • How can the frequency response of a BJT be engineered? 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]. Lecture 37-3 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 1. Common-emitter short-circuit current-gain cut-off frequency, fT fT : high-frequency figure of merit for transistors Short-circuit means from the small-signal point of view. BJT is biased in FAR. IC+ic IB+ib VCE ib IB Focus on small-signal current gain: h21 = ic |v =0 ib ce For low frequency, h21 → βF , for high frequency h21 rolls off due to capacitors. Definition of fT : frequency at which |h21 | = 1. 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 37-4 Small-signal equivalent circuit model: ic Cjc + ib vbe Cπ+Cje gπ gmvbe - ic = gmvbe − jωCjc ib = [gπ + jω(Cπ + Cje + Cjc )]vbe Then: h21 = gm − jωCjc gπ + jω(Cπ + Cje + Cjc) Magnitude of h21 : � |h21 | = � 2 + ω 2C 2 gm jc gπ2 + ω 2(Cπ + Cje + Cjc)2 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]. Lecture 37-5 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 � |h21 | = 2 + ω 2C 2 gm jc � gπ2 + ω 2(Cπ + Cje + Cjc)2 Bode plot of |h21 |: log |h21| βF -1 1 ωβ ωT ωc log ω Three regimes in |h21 |: • low frequency, ω  ωβ : |h21 |  gm = βF gπ • intermediate frequency, ωβ  ω  ωc: gm |h21 |  ω(Cπ + Cje + Cjc) • high frequency, ω  ωc: |h21 |  Cjc Cπ + Cje + Cjc 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 37-6 Angular frequencies that separate three regimes: ωβ = gπ Cπ + Cje + Cjc ωc = gm Cjc Angular frequency at which |h21 | = 1: ωT = gm Cπ + Cje + Cjc In terms of frequency: fT = gm 2π(Cπ + Cje + Cjc) Note: ωβ = ωT βF 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]. Lecture 37-7 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 � Physical meaning of fT 1/2πfT has units of time. Define delay time: τd = 1 Cπ Cje Cjc τtE Cje Cjc = + + = τtB + + + 2πfT gm gm gm βF gm gm Four delay components in τd. Consider response of BJT to a step-input base current: IC+ic ib,ic towards βF ib IB+ib ic VCE ib ib IB 0 τd t At t = 0 IB → IB + ib As t → ∞ VBE → VBE + vbe IC → IC + ic = IC + βF ib. 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]. Lecture 37-8 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 How much time does it take for iC to reach its final value? Charge must be delivered to four regions in BJT: • Quasi-neutral emitter qe = τtE ib • Quasi-neutral base qb = τtB ic • Emitter-base depletion region qje = Cjevbe = Cje ic gm • Base-collector depletion region qjc = Cjc vbc = Cjcvbe = Cjc ic gm Charge delivered at constant rate to base. Time that it takes for all charge to be delivered: τβ = qe + qb + qje + qjc Cje Cjc 1 = τtE + βF (τtB + + )= ib gm gm 2πfβ 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]. Lecture 37-9 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 How much time does it take for iC to build up to IC + ib? Since ic = βF ib, τd = τβ τtE Cje Cjc 1 = + τtB + + = βF βF gm gm 2πfT • τd = 1 : 2πfT delay time before iC increases to IC + ib • τβ = 1 : 2πfβ delay time before iC increases to IC + βF ib With sinusoidal input: ic Cjc + ib vbe gπ Cπ+Cje gmvbe - f ↑⇒ fraction of ib that goes into capacitors↑⇒ vbe ↓⇒ ic ↓. At fT : |ic| = |ib| 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]. Lecture 37-10 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 � Key dependencies of fT in ideal BJT  fT dependence on IC : Rewrite fT : fT = gm 1 1 = 2π(Cπ + Cje + Cjc) 2πτF 1 + kT Cje +Cjc qτ I F C Two limits: • Small IC : limited by depletion capacitances fT  IC q 2πkT Cje + Cjc • Large IC : limited by intrinsic delay (dominated by τtB ) fT  1 2πτF log fT 1 2πτF 1 log IC 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]. Lecture 37-11 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Alternative view of IC dependence: τd = τtE Cje Cjc 1 + τtB + + = βF gm gm 2πfT log t Cje gm Cjc gm td ttB ttE bF log IC Standard experimental technique to extract τF and Cje + Cjc: τd= 1 2πfT Cje+Cjc τF 0 0 1 = kT gm qIC 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]. Lecture 37-12 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007  fT dependence on VBC : VCB ↑ (B-C junction is more reverse biased) ⇒ Cjc ↓ ⇒ fT ↑ [but only in low IC regime of fT ] log fT 1 2πτF VCB log IC  fT dependence on device layout: • For low IC : fT dominated by Cje, Cjc Cje AE Cjeo ∝ gm IC Cjc AC Cjco ∝ gm IC If AE ↑ or AC ↑ (keeping IC constant) ⇒ fT ↓ • For high IC : fT dominated by τF ; fT independent of AE or AC 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 37-13 � Device design strategies for improving fT Four delay terms in fT : τd = 1 τtE Cje Cjc = + τtB + + 2πfT βF gm gm Strategies to reduce each delay component:  Emitter charging time, τtE , βF minimized by • enhancing βF , • having a shallow emitter (τtE ∼ WE2 ), • building steep doping profile in emitter. τtE βF small contribution to τd, not much payoff. 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 37-14  Base transit time, τtB , minimized by • reducing WB (τtB ∼ WB2 ), • introducing drift field in base (through impurity gradient or SiGe composition gradient). Significant device engineering towards minimizing τtB . Example 1 [Kasper 1993]: [Kasper, 1993] Kasper, E., and A. Gruhle. "Silicon Germanium Heterobipolar Transistor for High Speed Operation." Proceedings of the IEEE/Cornell Conference on Advanced Concepts in High Speed Semiconductor Devices and Circuits, August 2-4, 1993. New York, NY: IEEE Electron Devices Society, 1993, pp. 23-30. ISBN: 9780780308954. Copyright 1993 IEEE. Used with permission. 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 37-15 Example 2 [Yamazaki, IEDM 1990, p. 309]: Yamazaki, T., et al. "A 11.7 GHz 1/8-divider Using 43 GHz Si High Speed Bipolar Transistor with Photoepitaxially Grown Ultra-thin Base." Technical Digest of the International Electron Devices Meeting, San Francisco, CA, December 9-12, 1990. New York, NY: Institute of Electrical and Electronics Engineers, 1990, pp. 309-312. Copyright 1990 IEEE. Used with permission. Yamazaki, T., et al. "A 11.7 GHz 1/8-divider Using 43 GHz Si High Speed Bipolar Transistor with Photoepitaxially Grown Ultra-thin Base." Technical Digest of the International Electron Devices Meeting, San Francisco, CA, December 9-12, 1990. New York, NY: Institute of Electrical and Electronics Engineers, 1990, pp. 309-312. Copyright 1990 IEEE. Used with permission. 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]. Lecture 37-16 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Example 3 [Crabbé, IEDM 1990, p. 17]: (graded profile) (uniform profile) Crabbe, E. F., et. al. "Low Temperature Operation of Si and SiGe Bipolar Transistors." Technical Digest of the International Electron Devices Meeting, San Francisco, CA, December 9-12, 1990. New York, NY: Institute of Electrical and Electronics Engineers, 1990, pp. 17-20. Copyright 1990 IEEE. Used with permission. 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 37-17  E-B SCR charging time, Cje/gm: AE Cjeo Cjeo Cje ∝ = gm IC JC Minimized by: • NB ↓ • tailoring doping profiles at E-B junction  B-C SCR charging time, Cjc /gm: AC Cjco AC Cjco Cjc ∝ = gm IC AE JC Minimized by: • NC ↓ • tailoring doping profiles at B-C junction. • tightening layout of transistor: AC AE →1 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 37-18 Key conclusions • fT : high-frequency figure of merit for transistors: frequency at which |h21 | = 1. • fT of ideal BJT: fT = gm 2π(Cπ + Cje + Cjc) 1 : time it takes for step increase in iB to • Delay time, τd = 2πf T yield an identical step increase in iC . • Most effective ways to engineer fT : – reduce WB – introduce drift field in base (through impurity gradient or SiGe composition gradient) – tighten layout: AC AE →1 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].