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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 13-1 Lecture 13 - p-n Junction March 7, 2007 Contents: 1. Ideal p-n junction in equilibrium 2. Ideal p-n junction out of equilibrium Reading assignment: del Alamo, Ch. 7, §§7.1, 7.2 (7.2.1, 7.2.2) Announcements: Quiz 1: March 13, 7:30-9:30 PM; lec-tures #1-12 (up to SCR-type transport). Open book. Calculator required. Final Exam scheduled: May 23, 1:30-3:30 PM. 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 13-2 Key questions • What happens if you bring into intimate contact an n-type region and a p-type region? • What happens to the electrostatics of a p-n junction if one applies a bias accross? 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 13-3 Motivation: pn junctions everywhere! Example: CMOS PMOS n+ p+ n NMOS p+ n+ n+ p+ p n 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 13-4 1. Ideal p-n junction in equilibrium Eo Eo WSp WSn EFn EFp a) two semiconductors� far apart Eo Eo WSp WSn EFn EFp b) two semiconductors � just before contact Eo qφbi WSp WSn EF c) two semiconductors � in intimate contact 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 p Lecture 13-5 n Eo Eo χ WSp Ec WSn χ Ec EF EF Ev Ev Eo qφbi χ WSp Eo Ec WSn χ Ec EF Ev Ev qφbi = WSp − WSn = (EC − EF )|x�0 − (EC − EF )|x�0 no (x � 0) = kT ln no (x � 0) Then: φbi = kT ND NA ln q n2i 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 13-6 r qND 0 x 0 -qNA e 0 0 x 0 x metallurgical junction p - - - -- - -- - emax n + + ++ + ++ + + + + ++ + dipole of charge f 0 fbi log po, no NA ND po no ni2 ND ni2 NA 0 x 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 13-7 r depletion approximation exact qND -xp 0 xn 0 x -qNA e xn -xp 0 x 0 metallurgical junction p - - - - -- emax n + + ++ + + + + + + + ++ + dipole of charge f 0 fbi -xp xn 0 x log po, no NA ND po no ni2 ND ni2 NA 0 x 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 13-8 Do depletion approximation: � Volume charge density: ρ(x) ρ(x) ρ(x) ρ(x) � � � � 0 −qNA qND 0 in p-QNR: x < −xp in SCR: − xp < x < 0 in SCR: 0 < x < xn in n-QNR: xn < x � Electric field: E(x) � 0 qNA (x + xp) � qND E(x) � (x − xn) � E(x) � 0 E(x) � − in p-QNR: x ≤ −xp in SCR: − xp ≤ x ≤ 0 in SCR: 0 ≤ x ≤ xn in n-QNR: xn ≤ x � Electrostatic potential [select φ(x = 0) = 0]: φ(x) � φ(x) � φ(x) � φ(x) � qNAx2p − 2� qNA 2 (x + 2xpx) 2� qND 2 − (x − 2xnx) 2� qND x2 n 2� in p-QNR: x ≤ −xp in SCR: − xp ≤ x ≤ 0 in SCR: 0 ≤ x ≤ xn in n-QNR: xn ≤ x 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 13-9 Two unknowns: xn and xp . • demand overall charge neutrality: qNA xp = qND xn • potential difference across structure must be φbi: qND x 2n qNA x 2 p φ(xn) − φ(−xp) = + = φbi 2� 2� Solve for xn and xp : xn = � � � � � � 2�NA φbi qND (ND + NA ) xp = � � � � � � 2�ND φbi qNA(ND + NA ) Total SCR width: xSCR = � � � � � � 2�(ND + NA)φbi qNAND Maximum electric field: |Emax| = � � � � � � 2qNA ND φbi �(ND + NA ) 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 13-10 • symmetric junction: NA = ND : xp = xn |φ(−xp)| = φ(xn) • asymmetric junction: i.e. NA > ND : xp < xn |φ(−xp)| < φ(xn) • strongly asymmetric junction: i.e. p+-n junction NA � ND : xp � xn � xSCR � |Emax| � � � � � � � � � � � 2�φbi qND 2qND φbi � the lowly-doped side controls everything |φ(−xp)| � φ(xn) � φbi 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 13-11 ρ qND 0 0 xSCR x ε xSCR 0 0 x εmax φ φbi 0 0 xSCR x Ec EF Ev 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 13-12 2. Ideal p-n junction out of equilibrium Apply voltage across: • forward bias: p-region positive with respect to n-region • reverse bias: p-region negative with respect to n-region Voltage can drop in five distinct regions: • ohmic contact to n-region • quasi-neutral n-region • space-charge region • quasi-neutral p-region • ohmic contact to p-region 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 13-13 � Electrostatics Battery grabs on majority carrier Fermi levels [will see when we discuss ohmic contacts]. Application of voltage splits Fermi levels: Ec qφbi EF Ev p n Ec q(φbi-V) Efn V qV Efp Ev Ec q(φbi-V) Efp qV Efn Ev In forward and reverse bias: φbi → φbi − V 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 13-14 Qualitatively, electrostatics unchanged out of equilibrium, but SCR widens and shrinks, as needed: ρ qND -xp(V) 0 0 xn(V) x V>0 V=0 -qNA V<0 ε 0 0 x 0 x εmax(V) φ 0 φbi-V φbi φbi-V → use equilibrium equations: xSCR(V ) = � � � � � � |Emax(V )| = � � � � � 2�(ND + NA )(φbi − V ) V = xSCR(V = 0) 1 − qNAND φbi � � � � � � � � � � � 2qNA ND (φbi − V ) V = |Emax(V = 0)| 1 − �(ND + NA) φbi 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 13-15 � Depletion capacitance Think differentially: ρ qND ΔQ +Q -xp(V) 0 xn(V) ΔQ p - -Q n - - --- -- - - + + + ++ + ++ + + + + + + x V + + + + -qNA V+ΔV Δρ +ΔQ xn(V) 0 x -xp(V) −ΔQ C(V ) = � xSCR(V ) Then: C(V ) = � � � � � � �qNA ND C(V = 0) = � 2(ND + NA)(φbi − V ) 1 − φV bi 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 C(V ) = � � � � � � Lecture 13-16 �qNA ND C(V = 0) = � 2(ND + NA)(φbi − V ) 1 − φV bi For p+-n junction: C(V ) = � � � � � � �qND 2(φbi − V ) Capacitance dominated by lowly-doped side Technique to extract φbi and Nlow : 1 2(φbi − V ) = C2 �qND Q 1 C C2 - 2 εqN D φbi V 0 0 φbi V 0 φbi V 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 13-17 Experimental verification: Fortini, A., A. Hairie, and M. Gomina. "Analysis and Capacitive Measurement of the Built-in-field Parameter in Highly Doped Emitters." IEEE Transactions on Electron Devices 29, no. 10 (1982): 1604-1610. Copyright 1982 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 13-18 Key conclusions • Built-in potential of p-n junction: φbi = kT ND NA ln q n2i • Depletion approximation: two quasi-neutral regions separated by a space-charge region. • In strongly asymmetric junction electrostatics dominated by re­ gion with lowest doping level; i.e. for p+-n junction: xSCR � � � � � � 2�φbi qND |Emax| � � � � � � 2qND φbi � • Electrostatics out of equilibrium same as in TE if φbi ⇒ φbi − V . • Depletion capacitance due to SCR width modulation: C(V ) = � xSCR(V ) 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].
