6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 23-1 Lecture 23 - The Si surface and the Metal-Oxide-Semiconductor Structure (cont.) April 4, 2007 Contents: 1. Ideal MOS structure under bias (cont.) 2. Dynamics of the MOS structure Reading assignment: del Alamo, Ch. 8, §8.3 (8.3.5), §8.4 (8.4.1, 8.4.2) 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/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 23-2 Key questions • How sharply does the inversion layer ”turn on” and ”off” with the gate voltage? • How do the capacitance-voltage characteristics of the MOS struc-ture look like? • How do the C-V characteristics of a MOS structure depend on the frequency of the s mall signal? 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 23-3 1. MOS structure under bias (cont.) � Subthreshold regime In MOSFETs interested in current with the device nominally OFF, that is, for V < Vth: Subthreshold current MOS structure in depletion but fini te electron concentration at sur-face: 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].Courtesy of S. Mertens, MIT. Used with permission.� 6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 23-4 Compute Qe in d epletion: 2 �kT n� q�sNA qφs � exp Qe � − q NiA 2 � 2φs kT This key depend ence seen in exact solution: 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].Courtesy of S. Mertens, MIT. Used with permission.� � � � 6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 23-5 Express Qe in terms ov V by expanding φs around φsth: kT � q�sNA q(V − Vth) � exp Qe � − q 4φf nkT with: dV γ n = dφs|th � 1 + 2 � 2φf Note: n > 1 Key characteristic of subthreshold regime is inverse subthreshold slope: kT S = n ln 10 q At best, if n = 1, S = 60 mV/dec at room temperature. Typically, S = 80− 100 mV/dec. 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 23-6 2. Dynamics of the MOS structure • MOS structure looks and behaves like capacitor • C-V characteristics summarize complex behavior of MOS • C-V characteristics: powerful diagnostic tool of wide applicabil i ty Three key issu es to study: • impact of bias voltage • impact of f requency of s mall-signal • dy namic behavior un der fast changing condi tion s 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 23-7 � Q ualitative discuss ion first: M O S (p-type) ----------++ +++ + ++ + accumulationV<VFB flatbandV=VFB VFB<V<0 MO S V=0 V v 0<V<Vth V=Vth V>Vth -----+ + + ++ ----------+ ++ ++ + + -----------------------------------------------------++++ ++ + + ++++ ++ + + ++++ ++ + + ++ ++++++ + + ++ + -------------------------depletion zero bias depletion threshold inversion 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].Courtesy of S. Mertens, MIT. Used with permission.6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 23-8 � General defi nition of capacitance: dQg dQsC = = dV −dV After so me algebra: 1 C = 1 1+Cox Cs where Cs is defined as: dQsCs = −dφs Note: Cs > 0. Simple physical interpretation: M Cox Cs S 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 23-9 � Q uasi-static C-V characteristics If frequency of AC voltage signal is low en o ugh: qua si-static condi-tions use Poisson-Boltzmann formulation: ⇒Qs = −√2�skT NAF (φs) Then: Cs = dQs = √2�skT NA dF (φs) −dφs dφs This yields: �s 1 n2 i qφsCs = [(−exp −qφs + 1) + (expkT − 1)] √2LD F (φs) kT NA 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 23-10 Results of calculations for typical MOS structure: 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].Courtesy of S. Mertens, MIT. Used with permission.Courtesy of S. Mertens, MIT. Used with permission.6.720J/3.4 3J - Integrated Microelectroni c Devices - Spring 2007 Lecture 23-11 � Analytical approximations to C Accumulation • F (φs) � −exp −qφs 2kT Then: qCs � Cox(VF B − V )2kT For V sufficiently la rger than VF B, Cs becomes large, and: | | | |C � Cox Independent of V . Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare