Lecture 28  The Long MetalOxideSemiconductor FieldEffect Transistor (cont.) April 18, 2007


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1 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 281 Lecture 28  The Long MetalOxideSemiconductor FieldEffect Transistor (cont.) April 18, 2007 Contents: 1. Secondorder and nonideal effects Reading assignment: del Alamo, Ch. 9, 9.7
2 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 282 Key questions The potential of the inversion layer increases along the channel. This should change the local threshold voltage. Does this affect the IV characteristics of the MOSFET? What happens to MOSFET IV characteristics if we apply a bias to the body with respect to the source?
3 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture Secondorder and nonideal effects in MOSFETs Introduce four significant refinements to model: Body effect (impact of ydependence of V T ) Back bias (impact of V BS ) Channel length modulation (impact of V DS > V DSsat ) Subthreshold regime (channel conduction for V GS < V T )
4 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 284 Body effect In a MOSFET biased in linear or saturation regimes, channel voltage V (y) depends on position: voltage difference between channel and body V (y) V T (y) (increases along y) V V DS V DS <V DSsat V GS >V T S n+ G D ID 0 0 L y n+ n+ V BS =0 inversion layer depletion region V GS V(y) p 0 L y V GS B no body effect V T local gate overdrive V DS 0 L y V GS V(y) V GS with body effect V To local gate overdrive V DS V th (y) Dependence of V T (y) further debiases transistor: I D lower than ideal V DSsat lower than ideal 0 L y
5 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 285 Voltage dependence of V T : V T (V ) = V To + γ( φ sth + V φ sth ) V To is V T for V SB = 0. Charge control relation becomes: Q i = C ox (V GS V V T ) = C ox [V GS V V To γ( φ sth + V φ sth )] Insert into current equation: dv I e = Wµ e Q i dy dv = Wµ e C ox [V GS V V To γ( φ sth + V φ sth )] dy Integrate from y = 0 to y = L MOSFET current in linear regime: W 1 2 I D = µ e C ox {(V GS V To +γ φ sth V DS )V DS γ[(φ sth +V DS ) 3/2 (φ sth ) 3/2 ]} L 2 3 Note new terms multiplied by γ if γ 0, body effect 0.
6 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 286 To get V DSsat, look at Q i at y = L: Q i (y = L) = C ox [V GS V DSsat V To γ( φ sth + V DSsat φ sth )] = 0 Solve for V DSsat : γ 2 4 V DSsat = V GS V To + γ φ sth [ 1 + (VGS V FB ) 1] 2 γ 2 MOSFET saturated current: plug V Dssat into current equation in linear regime: W 1 I Dsat = µ e C ox {(V GS V To + γ φ sth V DSsat )V DSsat L γ[(φ sth + V DSsat ) 3/2 (φ sth ) 3/2 ]}
7 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 287 Three noticeable features: for all values of V GS and V DS, body effect reduces I D for given V GS, body effect reduces V DSsat body effect goes away as transistor is turned off
8 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 288 Key observations for model simplification: V DSssat dependence on V GS remains roughly linear: I Dsat dependence on V GS remains roughly quadratic:
9 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 289 Linearize dependence of V T on V (V φ sth ): γ V T (V ) = V To + γ( φ sth + V φ sth ) V To + V 2 φsth Solve again differential equation to get MOSFET current in linear regime: with: V DSsat becomes: W m I D µ e C ox (V GS V To V DS )V DS L 2 Current in saturation regime: γ m = 1 + > 1 2 φ sth 1 V DSsat (V GS V To ) m W I Dsat µ e C ox (V GS V To ) 2 2mL
10 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 2810
11 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture m is bodyeffect coefficient (m > 1): m = 1 + γ 2 φ sth m has same dependences as γ: x ox γ m (less severe body effect) N A γ m (more severe body effect) m and γ represent relative electrostatic influence of gate and body on inversion layer; if γ = 0 m = 1 (negligible impact of body). In circuit CAD, m used as fitting parameter. Typically m
12 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture Back bias If bias applied to body with respect to source (V SB > 0): V T shifts positive for constant V GS and V DS, I D reduced Model in absence of body effect just replace V T in first order model by: V T (V SB ) = V To + γ( φ sth + V SB φ sth )
13 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture 2813
14 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture IV characteristics of nchannel MOSFET (L = 1.5 µm) Output characteristics (V GS = 0 3 V, ΔV GS = 0.5 V ):
15 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture Transfer characteristics (V DS = 4 V ):
16 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture Output characteristics vs. back bias (V SB = 0, 2 V ):
17 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture Transfer characteristics vs. back bias (V DS = 4 V, V SB = 0 2 V, ΔV SB = 0.5 V ):
18 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture Backgate output characteristics (V SB = 0 3 V in 0.5 V increments, V GS = 1.5 V ):
19 6.720J/3.43J  Integrated Microelectronic Devices  Spring 2007 Lecture Key conclusions Body effect arises from spatial dependence of V T : local gate overdrive reduced. Main consequences of body effect: I D lower than ideal, V DSsat lower than ideal. Simple formulation of body effect is fairly accurate: with m 1. W I Dsat µ e C ox (V GS V To ) 2 2mL m captures relative electrostatic influence of gate and body (want m 1). Application of back bias shifts V T positive and reduces I D.
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