Lecture 8 MOSFET(I) MOSFET I-V CHARACTERISTICS

Transcription

1 Lecture 8 MOSFET(I) MOSFET I-V CHARACTERISTICS Outline 1. MOSFET: cross-section, layout, symbols 2. Qualitative operation 3. I-V characteristics Reading Assignment: Howe and Sodini, Chapter 4, Sections Announcement: Quiz#1, March 14, 7:30-9:30PM, Walker Memorial; covers Lectures #1-9; open book; must have calculator Spring 2007 Lecture 8 1

2 1. MOSFET: layout, cross-section, symbols ; ; ; gate contact gate interconnect n + polysilicon gate active area (thin oxide area) polysilicon gate contact metal interconnect A ; ; ; A ; ; ; ; ; ; ; ; source contacts W ; drain contacts bulk contact ; ; ; ; ; ; field oxide edge of source drain active area interconnect interconnect (a) gate oxide deposited bulk source n drain oxide + polysilicon gate interconnect interconnect interconnect L n + drain diffusion n + source diffusion L p + diff [ p-type ] Key elements: Inversion layer under gate (depending on gate voltage) Heavily doped regions reach underneath gate inversion layer to electrically connect source and drain 4-terminal device: body voltage important (b) ; ; Spring 2007 Lecture 8 2

3 Circuit symbols Two complementary devices: n-channel device (n-mosfet) on p-substrate uses electron inversion layer p-channel device (p-mosfet) on n-si substrate uses hole inversion layer G + I Dn V GS _ D + V DS > 0 B + _ V BS S G I Dn D S B _ G V SG I Dp + S + V SB _ B V SD > 0 D G I Dp S D B (a) n-channel MOSFET (b) p-channel MOSFET Drain n + Source p + Gate p Bulk or Body Gate n Bulk or Body Source n + Drain p Spring 2007 Lecture 8 3

4 2. Qualitative Operation Drain Current (I D ): proportional to inversion charge and the velocity that the charge travels from source to drain Velocity: proportional to electric field from drain to source Gate-Source Voltage (V GS ): controls amount of inversion charge that carries the current Drain-Source Voltage (V DS ): controls the electric field that drifts the inversion charge from the source to drain VDS VGS ID S G D n+ n+ depletion region inversion layer p B Want to understand the relationship between the drain current in the MOSFET as a function of gate-to-source voltage and drain-to-source voltage. Initially consider source tied up to body (substrate or back) Spring 2007 Lecture 8 4

5 Three Regimes of Operation: Cut-off Regime MOSFET: V GS < V T, with V DS 0 Inversion Charge = 0 V DS drops across drain depletion region I D = 0 S V GS <V T G V DS 0 D n+ n+ depletion region p no inversion layer anywhere Spring 2007 Lecture 8 5

6 Three Regimes of Operation: Linear or Triode Regime S V GS >V T G V GD >V T V DS 0 D n+ n+ depletion region p inversion layer everywhere V GD = V GS -V DS Electrons drift from source to drain electrical current! V GS Q N, I D V DS E y, I D V DS << V GS -V T Spring 2007 Lecture 8 6

7 Three Regimes of Operation: Saturation Regime V DS > V GS -V T V GS > V T, V GD < V T ---> V DS > V GS -V T S V GS >V T G V GD <V T D n+ n+ depletion region p inversion layer "pinched-off" at drain side I D is independent of V DS : I D =I dsat Electric field in channel cannot increase with V DS Spring 2007 Lecture 8 7

8 3. I-V Characteristics (Assume V SB =0) Geometry of problem: All voltages are referred to the Source General expression of channel current Current can only flow in the y-direction: Total channel current: I y = W Q N (y) v y (y) Drain current is equal to minus channel current: I D = W Q N (y) v y (y) Spring 2007 Lecture 8 8

9 I-V Characteristics (Contd.) I D = W Q N (y) v y (y) Re-write equation in terms of voltage at location y, V(y): If electric field is not too high: v y (y) = µ n E y (y) = µ n dv dy For Q n (y), use charge-control relation at location y: Q N (y) = C ox [ V GS V(y) V ] T for V GS V(y) V T.. Note that we assumed that V T is independent of y. See discussion on body effect in Section 4.4 of text. All together the drain current is given by: I D = W µ n C ox [ V GS V( y) V T ] dv(y) dy Simple linear first order differential equation with one un-known, the channel voltage V(y) Spring 2007 Lecture 8 9

10 I-V Characteristics (Contd..) Solve by separating variables: I D dy = W µ n C ox [ V GS V(y) V T ] dv Integrate along the channel in the linear regime subject the boundary conditions : - Source: y=0, V(0)=0 - Drain: y=l, V(L)=V DS (linear regime) Then: L I D 0 dy = W µ n C ox [ V GS V(y) V T ] dv Resulting in: I D y V DS 0 L [] 0 = ID L = W µ n C ox V GS V 2 V T V 0 V DS I D = W L µ nc ox V GS V DS 2 V T V DS Spring 2007 Lecture 8 10

11 I-V Characteristics (Contd ) I D = W L µ nc ox V GS V DS 2 V T V DS for V DS < V GS V T Key dependencies: V DS I D (higher lateral electric field) V GS I D (higher electron concentration) This is the linear or triode regime: It is linear if V DS <<V GS -V T Spring 2007 Lecture 8 11

12 I-V Characteristics (Contd.) Two important observations 1. Equation only valid if V GS V(y) V T at every y. Worst point is y=l, where V(y) = V DS, hence, equation is valid if V DS V GS V T Spring 2007 Lecture 8 12

13 I-V Characteristics (Contd..) Two important observations 2. As V DS approaches V GS V T, the rate of increase of I D decreases. Reason: As y increases down the channel, V(y), Q N (y), and E y (y) (fewer carriers moving faster) inversion layer thins down from source to drain I D grows more slowly Spring 2007 Lecture 8 13

14 I-V Characteristics (Contd ) Drain Current Saturation As V DS approaches V DSsat = V GS V T increase in E y compensated by decrease in Q N I D saturates when Q N equals 0 at drain end. Value of drain saturation current: I Dsat = I Dlin (V DS = V DSsat = V GS V T ) Then I Dsat = W L µ nc ox V GS V DS 2 V T V DS V DS =V GS V T I Dsat = 1 2 W L µ nc ox [ V GS V T ] 2 Will talk more about saturation regime next time Spring 2007 Lecture 8 14

15 I-V Characteristics (Contd.) Output Characteristics Transfer characteristics: Spring 2007 Lecture 8 15

16 Output Characteristics Spring 2007 Lecture 8 16

17 Summary of Key Concepts MOSFET Output Characteristics I-V Characteristics in Cutoff Regime V GS < V T I D = 0 I-V Characteristics in Linear Regime V DS < V GS -V T I D = W L µ nc ox V GS V DS 2 V T I-V Characteristics in Saturation Regime V DS V GS -V T V DS I Dsat = W 2L µ nc ox ( V GS V T ) Spring 2007 Lecture 8 17