# Lecture 9 MOSFET(II) MOSFET I V CHARACTERISTICS(contd.)

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1 Lecture 9 MOSFET(II) MOSFET I V CHARACTERISTICS(contd.) Outline 1. The saturation region 2. Backgate characteristics Reading Assignment: Howe and Sodini, Chapter 4, Section Spring 2009 Lecture 9 1

2 1. The Saturation Region Geometry of problem Regions of operation: Cut off: V GS < V T No inversion layer anywhere underneath the gate I = 0 D Linear: V GS >V T and 0 < V DS < V GS -V T : Inversion layer everywhere under the gate I D = W V DS L µ n C ox V GS V T V DS Spring 2009 Lecture 9 2

3 The Saturation Region (contd.) Saturation: V GS > V T, and V DS > V GS - V T : Inversion layer pinched-off at drain end of channel I D = W µ n C ox [V GS V T ] 2 2L Output characteristics: Last lecture: To derive the above equations for I D, we used for Q N (y), the charge-control relation at location y: Q N (y) = C ox [VGS V (y) V T ] for V GS V(y) V T.. Note that we assumed that (a) V BS = 0 V GS = V GB, and (b) V T is independent of y. See discussion on body effect in Section 4.4 of text Spring 2009 Lecture 9 3

4 The Saturation Region (contd..) Review of Q N, E y, and V in linear regime as V DS increases: Ohmic drop along channel de-biases inversion layer current saturation Spring 2009 Lecture 9 4

5 The Saturation Region (contd.) What happens when V DS = V GS V T? Charge control relation at drain: Q N (L) = C [ ox V GS V DS V T ]= 0 No inversion layer at the drain end of channel???!!! Pinch off. At pinch off: Charge control equation inaccurate around V T ; Electron concentration small but not zero; Electrons move fast because electric field is very high; Dominant electrostatic feature Acceptor charge There is no barrier to electron flow (on the contrary!) Spring 2009 Lecture 9 5

6 The Saturation Region (contd ) Voltage at pinch-off point (V=0 at source): Drain current at pinch-off: lateral electric field V DSsat = V GS V T electron concentration V GS V T I [ V V ] 2 Dsat GS T Also, L E y : 1 I Dsat L Spring 2009 Lecture 9 6

7 The Saturation Region (contd.) What happens if V DS > V GS V T? Depletion region separating pinch-off and drain widens To first order, I D does not increase past pinch-off: I = I W µc [V V ] 2 D Dsat n ox GS T 2L To second order, electrical channel length affected: L I D : 1 1 L I D 1 + L L L L Spring 2009 Lecture 9 7

8 The Saturation Region (contd.) Experimental finding: L = λ(vds V DSsat ) L with 1 λ L Typically, λ = 0.1 µm V L 1 For L = 1µm, increase of V DS of 1V past V DSsat results in increase in I D of 10%. Improved but approximate model for the drain current in saturation: I D W µ n C ox (V GS V T ) 2 [1+ λv DS ] 2L Spring 2009 Lecture 9 8

9 2. Backgate Characteristics There is a fourth terminal in a MOSFET: the body. What does it do? Key Assumption (thus far): V BS = 0 V GS = V GB Body contact allows application of bias to body with respect to inversion layer, V BS. Only interested in V BS < 0 (pn diode in reverse bias). Interested in effect on inversion layer examine for V GS > V T (keep it constant) Spring 2009 Lecture 9 9

10 Backgate Characteristics (Contd.) Application of V BS < 0 increases potential build-up across semiconductor: 2φ p 2φ p V BS Depletion region at the source must widen to produce required extra field: E s = (Q B +Q N ) ε s Spring 2009 Lecture 9 10

11 Backgate Characteristics (Contd.) Consequences of application of V BS < 0: -2φ p -2φ p - V BS Q B x dmax Since V GS is constant, V ox unchanged E ox unchanged Q S = Q G unchanged Q S = Q N + Q B unchanged, but Q B Q N inversion layer charge is reduced! V DS + - V GS + - Metal interconnect to gate n + polysilicon gate V BS = 0 n+ source y 0 n+ drain Q N (y) X d (y) x p-type Metal interconnect to bulk Figure by MIT OpenCourseWare. For the same applied gate-to-source voltage V GS, application of V BS < 0 reduces the density of electrons in the inversion layer, in other words V T Spring 2009 Lecture 9 11

12 Backgate Characteristics (Contd.) How does V T change with V BS? In V T formula change 2φ p to 2φ p V BS : V T GB (VBS ) = V FB 2φ p V BS + 1 C ox 2ε s qn a ( 2φ p V BS ) In MOSFETs, interested in V T between gate and source: V GB = V GS V BS V T GB = VT GS VBS Then: And: V GS = V GB +V T T BS V T GS (VBS ) = V FB 2φ p + 1 2ε s qn a ( 2φ p V BS ) V T (V BS ) C ox In the context of the MOSFET, V T is always defined in terms of gate to source voltage Spring 2009 Lecture 9 12

13 Backgate Characteristics (Contd.) 1 V T (V BS ) = V FB 2φ p + 2ε s qn a ( 2φ p V BS ) C ox Define backgate effect parameter [units: V 1/2 ]: And: Then: γ = 1 C ox 2ε s qn a V To = V T (V BS = 0) V T (V BS ) = V To + γ[ 2φ p V BS 2φ p ] Spring 2009 Lecture 9 13

14 Backgate Characteristics (Contd.) Triode Region V DS ~ 0.1V Spring 2009 Lecture 9 14

15 What did we learn today? Summary of Key Concepts MOSFET in saturation (V DS V DSsat ): pinch off point at drain-end of channel Electron concentration small, but Electrons move very fast; Pinch-off point does not represent a barrier to electron flow I Dsat increases slightly in saturation region due to channel length modulation Backbias affects V T of MOSFET Spring 2009 Lecture 9 15

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