6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 17-1 Lecture 17 - Metal-Semiconductor Junction March 14, 2007 Contents: 1. Ideal metal-semiconductor junction in TE 2. Ideal metal-semiconductor junction outside equilib-rium Reading assignment: del Alamo, Ch. 7, §§7.1, 7.2 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-2 Key questions • What happens when you bring together a metal a nd a semicon-ductor in intimate contact? • What happens in a metal-semiconductor junction when you ap-ply a voltage to the metal with respect to the semiconductor? • In a metal-semiconductor junction under bi a s, is there current flow? If so, how exactly does it happen? 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-3 1. Ideal metal-semiconductor junction in TE � First, ideal metal-metal junction in TE: WM2 WM1 Eo Eo EF1 EF2 WM2 WM1 Eo Eo EF1 EF2 a) two metals far apart b) two metals just before contact Eo EF WM1 WM2 qφbi c) two metals in intimate contact dipole charge at interface → built-in potential 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-4 Spatial extent of SCR in MM junction: a few nm 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-5 Can define local work function Think of photoelectric experiment vs. position: hυth WM1 WM2 metal 1 metal 2 hυ -x hυth metal 1 metal 2 WM1 WM2 x Can define local vacuum energy Eo Shape of Eo identical to potential energy ⇒ 1 φbi = (WM1 − WM2) q � Ideal metal-semiconductor junction in TE Energy band line up depends on choice of metal an d semiconductor. 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-6 Do metal/n-type semiconductor with WM > WS: WS = χ + qϕn Ev a) metal and semiconductor far apart Ec WM EF EF EoEo WS χ qϕ n WM EF Eo Ec EF Eo Ev WS χ qϕBn M S qφbi qϕ n b) metal and semiconductor in intimate contact 1 φbi = (WM − WS) q 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-7 Eo Eo WM WS χ qϕBn qφbi qϕn Ec EF EF Ev Most important parameter of MS junction: Schottky barri er height: qϕBn = WM − χ Also: qϕBn = qφbi + qϕn Warning: si mpl e theory not followed due to surface states ⇒ In p ractice, rely on measurements for qϕBn. Still can use: qϕBn = qφbi + qϕn Typical Schottky barrier height: qϕB ∼ 0.4 − 0.8 eV (depends on metal and doping type). 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-8 � Electrostatics in TE In semiconductor: • close to the M-S interface: space-charge region • farther away: quasi-neutral region depletion approximation x ρ 0 xd qND exact 0 εmax x 0 xd ε 0 x φ −φbi 0 xd0 log po, no po no ND ni2 ND x0 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-9 Do depletion ap proximation: • Volume charge density: ρ(x) � qND in SCR: 0 ≤ x < xd ρ(x) � 0 in QNR: xd < x • Electric field: qNDE(x) � (x − xd) in SCR: 0 ≤ x ≤ xd E(x) � 0 in QNR: xd ≤ x • Electrostatic potential, wi th φ(bulk) = 0: φ(x) = −qND(x 2 − 2xdx + x 2 d) in SCR: 0 ≤ x ≤ xd2� φ(x) = 0 in QNR: xd ≤ 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-10 xd obtained by demanding φ(0) = − φbi: � 2�φbi xd = � qND Maximum field: qNDxd � 2qNDφbi |Emax| = = Key dependencies: • ND ↑ → xd ↓→ |Emax| ↑ • φBn ↑ → xd ↑→ |Emax| ↑ Also i n TE, Bo l tzmann relation: qφ(x) no(x) = ND exp kT At x = 0: −qφbi no(0) = ND exp kT Depletion approximation valid if no(0) � ND, or φbi � 3kT , easy! q 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 17-11 2. Metal-semiconduc tor junction outside eq uilibrium Appl y voltage across: • forward bias: metal positive with respect to semiconductor • reverse bias: metal negative with respect to semiconductor [notation reversed for metal/p-semiconductor jun ction]