6.720J/3.43J - Integrated Microelectro nic 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 23,1:30-3:30PM. 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 Microelectro nic 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 Microelectro nic Devices - Spring 2007 Lecture 13-3 Motivation: p n junctions everywhere! Example: CMO S PMOS NMOS n+ p+ p+ n+ n+p+ n 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 Microelectro nic Devices - Spring 2007 Lecture 13-4 1. Ideal p-n junction in eq uilibrium WSp EFn EFp a) two semiconductors� far apart Eo Eo WSp WSn EFn EFp b) two semiconductors � just before contact Eo Eo WSn Eo qφbi EF WSn WSp 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 Microelectro nic Devices - Spring 2007 Lecture 13-5 pn Eo Eo χχWSn WSp Ec Ec EF EF Ev Ev Eo χ qφbi WSp EoEc χWSn Ec EF qφbi = WSp − WSn = (EC − EF)|x�0 − (EC − EF)|x�0 no(x � 0) = kT ln no(x � 0) Then: kT NDNAφbi = ln 2q ni Ev 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 Microelectro nic Devices - Spring 2007 Lecture 13-6 r qND 0 0 x -qNA p --------------++ + emax n + f + fbi 0 + + ++ +++ + + e 0 0 x metallurgical junction dipole of charge 0 x log po, no NA ND po no ni2 ni2 ND 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 Microelectro nic Devices - Spring 2007 Lecture 13-7 r depletion approximation qND exact -xp0 0 xn x -qNA p --------------++ + emax n + ++ + f + fbi 0 + + + +++ e -xp xn 0 0 x metallurgical junction dipole of charge -xp 0 xn x log po, no NA ND po no ni2 ni2 ND 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 Microelectro nic Devices - Spring 2007 Lecture 13-8 Do depletion approximation: � Volume charge density: ρ(x) � 0 in p-QNR: x < −xp ρ(x) � −qNA in SCR: − xp < x < 0 ρ(x) � qND in SCR: 0 < x < xn ρ(x) � 0 in n-QNR: xn < x � Electric field: E(x) � 0 in p-QNR: x ≤ −xp qNAE(x) � − (x + xp) in SCR: − xp ≤ x ≤ 0 qND E(x) � (x − xn) in SCR: 0 ≤ x ≤ xn E(x) � 0 in n -QNR: xn ≤ x � Electrostatic potential [select φ(x = 0) = 0]: qNAx2 φ(x) � −p in p -QNR: x ≤ −xp2� φ(x) � qNA(x 2 + 2xpx) in S CR: − xp ≤ x ≤ 0 2� φ(x) � −qND(x 2 − 2xnx) in S CR: 0 ≤ x ≤ xn2� qNDx2 φ(x) � n in n -QNR: xn ≤ x 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 Microelectro nic Devices - Spring 2007 Lecture 13-9 Two unknowns: xn and xp. • demand overall charge neutrality: qNAxp = qNDxn • potential difference across structure must be φbi: qNDx 2 n 2 qNAx p φ(xn) − φ(−xp) = + = φbi 2� 2� Solve for xn and xp: � 2�NAφbi � 2�NDφbi xn = � xp = � qND(ND + NA) qNA(ND + NA) Total SCR width: � 2�(ND + NA)φbi xSCR = � qNAND Maximum electric fi eld: � 2qNANDφbi |Emax| = � �(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 Microelectro nic 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: � 2�φbi xp � xn � xSCR � � qND � 2qNDφbi |Emax| � the lowly-do ped 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 Microelectro nic Devices - Spring 2007 Lecture 13-11 x ρ 0 xSCR qND 0 εmax x 0 ε 0 xSCR x φ φbi 0 0 xSCR Ec Ev EF 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