Lecture 23 - The Si surface and the Metal-Oxide-Semiconductor Structure (cont.) April 4, 2007
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1 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 231 Lecture 23 The Si surface and the MetalOxideSemiconductor 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)
2 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 232 Key questions How sharply does the inversion layer turn on and off with the gate voltage? How do the capacitancevoltage characteristics of the MOS structure look like? How do the CV characteristics of a MOS structure depend on the frequency of the small signal?
3 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture MOS structure under bias (cont.) Subthreshold regime In MOSFETs interested in current with the device nominally OFF, that is, for V < V th : Subthreshold current MOS structure in depletion but finite electron concentration at surface: Courtesy of S. Mertens, MIT. Used with permission.
4 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 234 Compute Q e in depletion: 2 i 2 A kt n qɛ s N A Q e q N 2φ s qφ s exp kt This key dependence seen in exact solution: Courtesy of S. Mertens, MIT. Used with permission.
5 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 235 Express Q e in terms ov V by expanding φ s around φ sth : kt qɛ s N A q(v V th ) Q e exp q 4φ f nkt with: n = dv th 1 dφ s 2 γ 2φ f 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 = mv/dec.
6 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture Dynamics of the MOS structure MOS structure looks and behaves like capacitor CV characteristics summarize complex behavior of MOS CV characteristics: powerful diagnostic tool of wide applicability Three key issues to study: impact of bias voltage impact of frequency of smallsignal dynamic behavior under fast changing conditions
7 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 237 Qualitative discussion first: V<V FB M O S (ptype) accumulation V=V FB flatband MO S V FB <V<0 depletion V=0 zero bias V v 0<V<Vth V=Vth V>Vth depletion threshold inversion Courtesy of S. Mertens, MIT. Used with permission.
8 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 238 General definition of capacitance: dq g C = = dv dq s dv After some algebra: 1 C = 1 1 C ox C s where C s is defined as: dq s C s = dφs Note: C s > 0. Simple physical interpretation: M C ox Cs S
9 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 239 Quasistatic CV characteristics If frequency of AC voltage signal is low enough: quasistatic conditions use PoissonBoltzmann formulation: Q s = 2ɛ s ktn A F(φ s ) Then: This yields: C s = dq s = 2ɛs ktn A df(φ s ) dφs dφ s ɛ s 1 qφ n 2 i qφ s C s = s [( exp 1) (exp 1)] 2 2LD F(φ s ) kt N A kt
10 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2310 Results of calculations for typical MOS structure: Courtesy of S. Mertens, MIT. Used with permission. Courtesy of S. Mertens, MIT. Used with permission.
11 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2311 Analytical approximations to C Accumulation Then: F(φ s ) exp qφ s 2kT q C s C ox (V FB V ) 2kT For V sufficiently larger than V FB, C s becomes large, and: C C ox Independent of V.
12 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2312 Depletion qφ s F(φ s ) kt Which yields: C s C ox V 1 4 V γ 2FB 1 Overall capacitance: C C ox 1 4 V γ VFB 2 Squareroot dependence on V.
13 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2313 Inversion F(φ) n i N A exp qφ 2kT This results in: q C s C ox (V V th ) 2kT For V sufficiently larger than V th, C s is large and: C C ox Independent of V.
14 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2314 Highfrequency CV characteristics Time constants associated with charge modulation in semiconductor: Accumulation: hole concentration modulated in accumulation layer (majority carriers) τ max(τ d, RC) Depletion: hole concentration modulated at edge of depletion layer (majority carriers) τ max(τ d, RC) Inversion: electron concentration modulated in inversion layer (minority carriers) τ τ g with τ g generation lifetime. For highfrequency AC signals, inversion layer can t keep up: CV characteristics modified in inversion.
15 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2315 Evolution of ΔQ in inversion for LF and HF: ρ ΔQg=ΔQs x dmax 0 xox 0 x at HF ΔQs=ΔQ d at LF ΔQ s =ΔQ i At lowfrequency: At highfrequency: ΔQ s ΔQ i Since x d x dmax, ΔQ s ΔQ d C s,hf C s,dep (V th ) γc ox 2 2φ f C sth
16 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2316 CV characteristics: C C ox low frequency high frequency V Experimental highfrequency CV characteristics: 90.0p 80.0p 70.0p C (F) 60.0p 400 Hz 500 Hz 50.0p 40.0p 30.0p 800 Hz 1 khz 2 khz 1 MHz V (V) Image by MIT OpenCourseWare. Adapted from an image by Tassanee Payakapan, MIT.
17 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2317 Key conclusions In subthreshold regime, inversion charge drops exponentially with V below threshold: Inverse subthreshold slope: qφ s q(v V th ) Q e exp exp kt nkt kt S = n q ln mv/dec at 300 K Typical inverse subthreshold slope of well designed MOSFETs at 300 K: S mv/dec. MOS capacitance: series of oxide capacitance and semiconductor capacitance: For lowfrequency excitation: = C C ox C s C(acc) C(inv) C ox
18 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 2318 Self study General derivation of CV characteristics from PoissonBoltzmann formulation. Algebra behind analytical approximations for capacitancevoltage characteristics in accumulation, depletion and inversion.
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