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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 36-1 Lecture 36 - Bipolar Junction Transistor (cont.) May 4, 2007 Contents: 1. Current-voltage characteristics of ideal BJT (cont.) 2. Charge-voltage characteristics of ideal BJT 3. Small-signal behavior of ideal BJT Reading material: del Alamo, Ch. 11, §§11.2 (11.2.5), 11.3, 11.4 (11.4.1) 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 36-2 Key questions • How do the output characteristics of the ideal BJT look like? • How do the charge-voltage characteristics of the ideal BJT look like? • What is the topology of the small-signal equivalent circuit model of the ideal BJT in FAR? • What are the key dependencies of its elements? 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 36-3 1. Current-voltage characteristics of ideal BJT (cont.) Ideal BJT current equations (superposition of forward active + re­ verse): qVBE qVBC IS qVBC − exp ) − (exp − 1) kT kT βR kT IS qVBE IS qVBC = (exp − 1) + (exp − 1) βF kT βR kT IS qVBE qVBE qVBC = − (exp − 1) − IS (exp − exp ) βF kT kT kT IC = IS (exp IB IE Equivalent circuit model representation: C qVBC IS (exp -1) kT βR B IS (exp qV qVBE - exp BC ) kT kT qVBE IS (exp -1) kT βF E Complete model has only three parameters: IS , βF , and βR. 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 36-4 � Common-emitter output I-V characteristics vs. VCB : IC B C + + VCE + VBE - forward active saturation VBC - IB IB=0 E 0 0 cut-off VCB VBC,on vs. VCE : IC B C + + VCE + VBE - forward active saturation VBC - IB IB=0 E 0 reverse 0 cut-off VCE=VCB+VBE VCE,sat VCEsat = −VBCon + VBEon 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 36-5 IC vs. VCB with IB as parameter: 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 36-6 Where is the reverse regime? 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 36-7 Common-emitter output characteristics: 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 36-8 Zoom into inverse regime: 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 36-9 2. Charge-voltage characteristics of ideal BJT In BJT, two types of stored charge: • depletion layer charge • minority carrier charge In forward-active regime: B E depletion charge� in base-emitter SCR C B depletion charge� in base-collector � SCR B E B minority carrier � charge in� minority carrier � emitter QNR charge in� base QNR� � C 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 36-10 � Depletion layer charge In B-E and B-C SCR’s, respectively: QjE = AE � � � � � 2�qNE NB (φbiE − VBE ) NE + NB QjC = AC � � � � � 2�qNB NC (φbiC − VBC ) NB + NC φbiE and φbiC are respective built-in potentials. Since NE � NB � NC , � QjE � AE 2�qNB (φbiE − VBE ) � QjC � AC 2�qNC (φbiC − VBC ) Depletion capacitance: Cje = Cjc = � � � � � E � �qNB Cjeo =� 2(φbiE − VBE ) 1 − VφBE � � � � � C � �qNC Cjco =� 2(φbiC − VBC ) 1 − VφBC ∂QjE �A ∂VBE ∂QjC �A ∂VBC biE biC 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 36-11 � Minority carrier charge Excess minority carriers in QNR’s ⇒ excess majority carriers to keep quasi-neutrality ⇒ diffusion capacitance. Key result from pn diode: in ”short” or ”transparent” QNR: stored charge = minority carrier transit time × injected minority carrier current • For emitter in FAR: pE pE(VBE) IB QE ni2 NE -WE-xBE -xBE x QE = τtE IB with hole transit time: τtE WE2 = 2DE 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 36-12 • For base in FAR: nB nB(VBE) IC QB nB(WB)=0 ni2 NB WB 0 x QB = τtB IC with electron transit time: τtB WB2 = 2DB 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 36-13 Comments: • Units of QE and QB are C. • QE and QB scale with AE . Total minority carrier charge in FAR: QF = QE + QB = τtE IB + τtB IC = ( τtE + τtB )IC = τF IC βF τF ≡ intrinsic delay [s] τF is overall time constant for minority carrier storage in BJT in FAR: τF = τtE + τtB βF Note: emitter contribution to τF is τtE /βF because IB is βF times smaller than IC . If VBE changes, QE and QB change ⇒ capacitive effect: CF = qIC dQF = τF dVBE kT 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 36-14 Location of this capacitance? Think of which terminals supply stored charge (minority and majority carriers): For QE : • minority carriers (holes) injected from base • majority carriers (electrons) come from emitter contact For QB : • minority carriers (electrons) injected from emitter • majority carriers (holes) come from base contact Equivalent-circuit model: C QjC IS exp B QF QjE qVBE kT qVBE IS (exp -1) kT βF E 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 36-15 Similar picture in reverse regime: charge storage in base and collector Q R = τ R IE τR a bit complicated because it accounts for charge storage in in­ trinsic and extrinsic base and collector regions. B E B minority carrier � charge in� base QNR� � minority carrier � charge in� collector QNR C Diffusion capacitance: CR = qIE dQR = τR dVBC kT Located between base and collector terminals. 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 36-16 By superposition, complete equivalent circuit model valid in all four regimes: C QR QjC qVBC IS (exp -1) kT βR IS (exp B QF QjE qV qVBE - exp BC ) kT kT qVBE IS (exp -1) kT βF E 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 36-17 3. Small-signal behavior of ideal BJT In analog (and digital) applications, interest in behavior of BJT to small-signal applied on top of bias ⇒ small-signal equivalent circuit model. � Small-signal equivalent circuit model in FAR Must linearize hybrid-π model in FAR: C QjC IS exp B QF QjE qVBE kT qVBE IS (exp -1) kT βF E -Non-linear voltage-controlled current source linearized to linear voltage­ controlled current source. -Diode linearized to resistor. -Charge storage elements linearized to capacitors. 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 36-18 • Linearized voltage-controlled current source Apply small signal vbe on top of bias VBE . n nB(VBE+vbe) nB(VBE) IC+ic IC nB(WB)=0 WB 0 x Collector current: IC +ic = IS exp q(VBE + vbe ) qVBE qvbe qvbe � IS exp (1+ ) = IC (1+ ) kT kT kT kT Small-signal collector current: ic = qIC vbe kT Define transconductance: gm = qIC kT gm depends only on absolute value of IC and T (unlike MOSFET, where gm depends on device geometry) 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 36-19 • Linearized diode p pE(VBE+vbe) pE(VBE) IB+ib IB ni2 NE -WE-xBE -xBE x Base current: IB + ib = IS exp q(VBE + vbe ) IS qVBE qvbe � exp (1 + ) kT βF kT kT Small-signal base current: ib = qIB vbe kT Define conductance: gπ = qIB q IC gm = = kT kT βF βF Then, in general, gπ � gm 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 36-20 • Capacitors QjE → Cje QjC → Cjc QF → Cπ = τF qIC kT Two components in Cπ : pE pE(VBE+vbe) nB ΔQB ΔQE nB(VBE+vbe) pE(VBE) IB+ib nB(VBE) IC+ic IB ni2 NE -WE-xBE -xBE IC x 0 nB(WB)=0 WB x Note: Cπ = τF gm 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 36-21 • Small-signal equivalent circuit model for ideal BJR in FAR: Cjc B C + vbe Cπ+Cje gπ gmvbe E 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 36-22 Key conclusions • In BJT, two types of stored charge: depletion layer charge and minority carrier charge. • Depletion layer charge accounted through depletion capacitances. • Minority carrier charge accounted through time constant τF (in­ trinsic delay): τF = τtE + τtB βF Emitter contribution to τF is βF times smaller than τtE because IB is βF times smaller than IC . • Non-linear hybrid-π model for ideal BJT including charge stor­ age elements: C QR QjC qVBC IS (exp -1) kT βR IS (exp B QF QjE qV qVBE - exp BC ) kT kT qVBE IS (exp -1) kT βF E 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 36-23 • Small-signal equivalent circuit model of ideal BJT in FAR: Cjc B C + vbe Cπ+Cje gπ gmvbe E with: gm = qIC kT gπ = qIB gm = kT βF Cπ = τF gm 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].
