6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-1 Lecture 29 - The Long Metal-Oxide-Semiconductor Field-Effect Transistor (cont.) April 20, 2007 Contents: 1. Non-ideal and second-order effects (cont.) Reading assignment: del Alamo, Ch. 9, 9.7.3, 9.7.4
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-2 Key questions The MOSFET current in the saturation regime is not perfectly saturated. Why? What are the key dependencies of the output conductance? What is the physics of carrier transport in the subthreshold regime? What are the key dependencies of the subthreshold current? Why is the subthreshold current important?
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-3 1. Second-order and non-ideal effects in MOSFET (cont.) Channel length modulation Output characteristics of n-mosfet (2N7000): Note: small but distinct slope in I D V DS characteristics in saturation regime slope increases with V GS
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-4 Origin is channel length modulation: To first order, in saturation, V DS no longer controls the electrostatics of the channel I D saturates with further increases in V DS However, increases in V DS beyond V DSsat must be accommodated somehow depletion region opens up at drain-end of channel: G n+ D n+ p inversion layer depletion region l p L y As V DS V DSsat : effective channel length shortens: L L l p lateral field in channel I D : imperfect saturation
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-5 Lateral electrostatics in pinch-off region: ρ(y) qn D L-l p L -qn A 0 0 qn(x=0) y ε y (y) ε p ε max 0 0 L-l p L y V(y) V DS V DS -V DSsat V DSsat 0 0 L-l p L y To model Channel Length Modulation, need model for l p vs. V DS.
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-6 Main result (see details in notes): l p V DS V DSsat E p where E p is peak field at the pinch-off point: E p q V DSsat kt 2L Note key dependencies: At pinchoff, when V DS = V DSsat, l p = 0 l p linear on V DS V DSsat l p L
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-7 Impact on I D Since: I Dsat 1 L Then, channel length modulation implies: 1 1 1 l p 1 V DS V DSsat I Dsat = l (1 + ) = (1 + ) L l p L(1 p ) L L L E p L L Assumed that in well designed device l p L Define λ as Channel Length Modulation Parameter (units V 1 ): λ = 1 E p L Then: W I Dsat µ e C ox (V GS V T ) 2 [1 + λ(v DS V DSsat )] 2L λ is a parameter characteristic of the technology
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-8 W I Dsat µ e C ox (V GS V T ) 2 [1 + λ(v DS V DSsat )] 2L Features of new term: goes to zero for V DS = V DSsat proportional to I Dsat slope of I D V DS characteristics increases the higher V GS ID VDSsat VGS 0 0 VDS VGS=VT In analogy with BJT, 1/λ sometimes referred to as Early voltage.
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-9 Output conductance: slope in I D in saturation regime: I Dsat g o = λi Dsat V DS V GS,V BS Important result: for a given technology, g o only depends on I Dsat : g o I Dsat g o linear V GS impact of channel-length modulation 0 0 saturation cut-off VDS
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-10 Output conductance of 2N7000 n-mosfet:
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-11 Subthreshold regime Output characteristics of MOSFET in saturation in semilog scale: Transfer characteristics of MOSFET in saturation in semilog scale:
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-12 Experimental observations below threshold: I D exponential on V GS I D saturated with V DS down to very small values of V DS q(v GS V T ) I D exp nkt log I D VDS>VDSsat S -1 I off 0 VT VGS subthreshold regime
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-13 Two key figures of merit of subthreshold regime: Inverse subthreshold slope, S: voltage required to increase I D by 10X: S = nkt ln10 q If n = 1, S = 60 mv/dec at 300 K. Want S small to shut off MOSFET quickly. In well designed devices, S 70 90 mv/dec at 300 K. Off current, I off : I off = I D (V GS = 0) For logic CMOS, want I off in na range. I off set by S and V T.
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-14 Subtreshold current: MOS structure in weak inversion regime (below threshold). Inversion charge depends exponentially on V GS : with kt q(v V T ) Q e (V ) C sth exp q nkt n = 1 + C sth C ox The subthreshold current shows the dependencies of Q e in weakinversion regime. But, how does this charge flow from source to drain?
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-15 In weak inversion, dominant electrostatic feature is depletion region under gate electron Fermi level in drain, does not grab on electron Fermi level in inversion layer (there is no inversion layer!) Potential distribution under gate set by voltage on gate and not drain: V DS V GS <V T G ID Q e (0) Q e (L) S n+ D V BS =0 n+ weak electron concentration depletion region n+ E C qv DS E c (V DS =0) E fe (V DS =0) p 0 L y V DS E c (V DS ) E fe (V DS ) B In subthreshold regime: no longitudinal field in channel energy band diagram looks like the base of bipolar transistor electrons flow from source to drain by diffusion Diffusion current: dq e I D = WD e dy
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-16 No recombination along channel profile is linear in y: Q e (y = L) Q e (y = 0) I D = WD e L On the source side, V = V GS : kt q(v GS V T ) Q e (y = 0) C sth exp q nkt On the drain side, V = V GD = V GS V DS : All together: kt q(v GS V DS V T ) Q e (y = L) C sth exp q nkt W kt q(v GS V T ) qv DS I D D e C sth exp (1 exp ) L q nkt nkt
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-17 W kt q(v GS V T ) qv DS I D D e C sth exp (1 exp ) L q nkt nkt Notice: V DS = 0 I D = 0. If V DS kt q : W kt q(v GS V T ) I D D e C sth exp L q nkt with: γ n = 1 + = 1 + 2 2φ f C ox Key dependencies of subthreshold slope: C sth x ox C ox n sharper subthreshold. N A C sth n softer subthreshold. V SB C sth n sharper subthreshold. T softer subthreshold. n reflects electrostatic competition between top gate and body ( bottom gate )
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-18 Effect of N A : Figure removed due to copyright restrictions. Yang, Edward S. Microelectronic Devices. New York, NY: McGraw-Hill, 1988, p. 268. ISBN: 9780070722385.
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-19 Effect of V SB : Figure removed due to copyright restrictions. Sze, S. M. Physics of Semiconductor Devices. 2nd ed. New York, NY: Wiley, 1981, p. 448. ISBN: 9780471056614.
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-20 Effect of T: Figure removed due to copyright restrictions. Sze, S. M. Physics of Semiconductor Devices. 2nd ed. New York, NY: Wiley, 1981, p. 453. ISBN: 9780471056614.
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-21 Subthreshold regime important because it determines off current, I off : W kt qv T I off = I D (V GS = 0, V DS = V DD ) D e C sth exp L q nkt To get I off : L performance V T performance n N A short-channel effects x ox field in oxide I off : key goal in logic device design
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-22 I off important because it contributes to DC power dissipation in CMOS: V DD V IN =0 V OUT =V DD I off C L W off = I off V DD Example: I off = 100 pa/µm, W = 5 µm, V DD = 3.3 V W off = 1.7 nw. If 10 7 transistors W off = 17 mw. I off thermally activated: T I off W off. Same example with V th = 0.7 V and S 1 = 75 mv/dec @ 75 o C: W off (75 o C) = 74 W off (25 o C) = 1.1 W
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 29-23 Key conclusions Channel length modulation: as V DS > V DSsat, depletion region widents at drain-end of channel L I Dsat (imperfect saturation). Rough model: W I Dsat µ e C ox (V GS V T ) 2 [1 + λ(v DS V DSsat )] 2L Output conductance due to channel length modulation: g o I Dsat Subthreshold regime: I D drops off exponentially below V T : Inverse subthreshold slope: q(v GS V T ) I D exp nkt C sth kt S = (1 + ) ln 10 q C ox Off current of CMOS, I D (V GS = 0, V DD = 0), set by subthreshold regime. Important for static power dissipation.