Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 11: September 22, 2014 MOS Transistor Operating Regions Part 2

Today Operating Regions (continued) –Resistive –Saturation –Velocity Saturation –Subthreshold Drain Induced Barrier Lowering Penn ESE370 Fall DeHon 2

Last Time… Penn ESE370 Fall DeHon 3

Channel Evolution Increasing Vgs Penn ESE370 Fall DeHon 4

Threshold Voltage where strong inversion occurs  threshold voltage –Around 2 ϕ F –Engineer by controlling doping (N A ) Penn ESE370 Fall DeHon 5

Resistive Region V GS >V T, V DS small Penn ESE370 Fall DeHon 6

Channel Field When voltage gap V G -V x drops below V T, drops out of inversion –Occurs when: V GS -V DS < V T –Channel is “pinched off” –Current will flow, but cannot increase any further Penn ESE370 Fall DeHon 7

Saturation V DS > V GS -V T Penn ESE370 Fall DeHon 8

9 Blue curve marks transition from Linear to Saturation Saturation Region

New Stuff Penn ESE370 Fall DeHon 10

Preclass 1 What is electrical field in channel? –L eff =25nm, V DS =1V –Field = V DS /L eff Velocity: v=F*μ –Electron mobility: μ n = 500 cm 2 /(V  s) What is electron velocity? Penn ESE370 Fall DeHon 11

Same Phenomena I = (1/R) × V I increases linearly in V What’s I? –  Q/  t –Speed at which charge moves F=V/L v=  ×F=(  /L) ×V Velocity increases linearly in V What’s a moving electron? Penn ESE370 Fall DeHon 12

Short Channel Model assumes carrier velocity increases with field –Increases with voltage Are there limits to how fast things (including electrons) can move? Penn ESE370 Fall DeHon 13 S D

Short Channel Model assumes carrier velocity increases with field –Increases with voltage There is a limit to how fast carriers can move –Limited by scattering to 10 5 m/s < speed-of-light How relate to preclass 1b velocity? Encounter when channel short –Modern processes, L is short enough Penn ESE370 Fall DeHon 14 S D

Velocity Saturation At what voltage do we hit the speed limit? (preclass 1c) This is V dsat –The voltage at which velocity (current) saturates Penn ESE370 Fall DeHon 15

Velocity Saturation Once velocity saturates: Penn ESE370 Fall DeHon 16

Velocity Saturation Once velocity saturates: Can still increase current with parallelism –W – make it wider –V gs -V t – make it deeper Penn ESE370 Fall DeHon 17 S D

Velocity Saturation How does this V dsat compare to the threshold we have been using? Penn ESE370 Fall DeHon 18

Velocity Saturation Penn ESE370 Fall DeHon 19

Subthreshold Penn ESE370 Fall DeHon 20

Below Threshold Transition from insulating to conducting is non-linear, but not abrupt Current does flow –But exponentially dependent on V GS Penn ESE370 Fall DeHon 21

Subthreshold Penn ESE370 Fall DeHon 22

Subthreshold W/L dependence follow from resistor behavior (parallel, series) –Not shown explicitly in text λ is a channel width modulation effect Penn ESE370 Fall DeHon 23 S D

Steady State What current flows in steady state? What causes (and determines) the magnitude of current flow? Which device? Penn ESE370 Fall DeHon 24

Leakage Call this steady-state current flow leakage Ids leak Penn ESE370 Fall DeHon 25

Subthreshold Slope Exponent in V GS determines how steep the turnoff is –Every S Volts –Divide I DS by 10 Penn ESE370 Fall DeHon 26

Subthreshold Slope Exponent in V GS determines how steep the turnoff is –Every S Volts ( S not related to source ) –Divide I DS by 10 n – depends on electrostatics –n=1  S=60mV at Room Temp. (ideal) –n=1.5  S=90mV –Single gate structure showing S=90-110mV Penn ESE370 Fall DeHon 27

I DS vs. V GS Penn ESE370 Fall DeHon 28

Subthreshold Slope If S=100mV and V th =300mV, what is Ids(Vgs=300mV)/Ids(Vgs=0V) ? What if S=60mV? Penn ESE370 Fall DeHon 29

Threshold Penn ESE370 Fall DeHon 30

Threshold Describe V T as a constant Induce enough electron collection to invert channel Penn ESE370 Fall DeHon 31

V DS impact In practice, V DS impacts state of channel Penn ESE370 Fall DeHon 32

V DS impact Increasing V DS, already depletes portions of channel Penn ESE370 Fall DeHon 33

V DS impact Increasing V DS, already depletes portions of channel Need less charge, less voltage to invert Penn ESE370 Fall DeHon 34

Drain-Induced Barrier Lowering (DIBL) Penn ESE370 Fall DeHon 35 VTVT V DS

DIBL Impact Penn ESE370 Fall DeHon 36

In a Gate? What does it impact most? –Which device, has large Vds? Vin=Vdd ? Vin=Gnd ? –How effect operation? Speed of switching? Leakage? Penn ESE370 Fall DeHon 37

In a Gate V DS largest for off device –Easier to turn on Penn ESE370 Fall DeHon 38

In a Gate V DS largest for off device –Easier to turn on –Leak more Penn ESE370 Fall DeHon 39

PMOS Similar phenomena to NMOS Signs different –Negative V th –turn on when less than this Reason based on carriers Penn ESE370 Fall DeHon 40

Approach Identify Region Drives governing equations Use to understand operation Penn ESE370 Fall DeHon 41

Big Idea 3 Regions of operation for MOSFET –Subthreshold –Resistive –Saturation Pinch Off Velocity Saturation –Short channel Penn ESE370 Fall DeHon 42

Admin Text – highly recommend read –Finish it up on Wednesday Office Hours: M, T, W HW4 due Thursday Midterm 1 next Monday –Midterms from 2010, 2011, 2012, 2013 All online … both with and without answers Suggest start without answers Penn ESE370 Fall DeHon 43