Lecture 28 - The Long Metal-Oxide-Semiconductor Field-Effect Transistor (cont.) April 18, 2007

Transcription

1 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-1 Lecture 28 - The Long Metal-Oxide-Semiconductor Field-Effect Transistor (cont.) April 18, 2007 Contents: 1. Second-order and non-ideal effects Reading assignment: del Alamo, Ch. 9, 9.7

2 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-2 Key questions The potential of the inversion layer increases along the channel. This should change the local threshold voltage. Does this affect the I-V characteristics of the MOSFET? What happens to MOSFET I-V 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 Second-order and non-ideal effects in MOSFETs Introduce four significant refinements to model: Body effect (impact of y-dependence 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 28-4 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 28-5 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 28-6 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 28-7 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 28-8 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 28-9 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 28-10

11 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture m is body-effect 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 28-13

14 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture I-V characteristics of n-channel 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.