Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 10: September 20, 2013 MOS Transistor Operating Regions Part 1

Today MOS Transistor Topology Threshold Operating Regions –Resistive –Saturation –Velocity Saturation –Subthreshold Penn ESE370 Fall DeHon 2

Last Time Penn ESE370 Fall DeHon 3

Depletion region  excess carriers depleted Penn ESE370 Fall DeHon 4 Refinement

Body Contact Fourth terminal Also effects fields Usually common across transistors Penn ESE370 Fall DeHon 5

No Field V GS =0, V DS =0 Penn ESE370 Fall DeHon 6

Apply V GS >0 Accumulate negative charge –Repel holes (fill holes) Penn ESE370 Fall DeHon

Channel Evolution Increasing Vgs Penn ESE370 Fall DeHon 8

Gate Capacitance Penn ESE370 Fall DeHon 9 Changes based on operating region.

Inversion Surface builds electrons –Inverts to n-type –Draws electrons from n + source Penn ESE370 Fall DeHon 10

Threshold Voltage where strong inversion occurs  threshold voltage –Around 2 ϕ F –Engineer by controlling doping (N A ) Penn ESE370 Fall DeHon 11

Resistive Region V GS >V T, V DS small Penn ESE370 Fall DeHon 12

Resistive Region V GS >V T, V DS small V GS fixed  looks like resistor –Current linear in V DS Penn ESE370 Fall DeHon 13

Linear (Resistive) Region Penn ESE370 Fall DeHon 14

Penn ESE370 Fall DeHon 15 Blue curve marks transition from Linear to Saturation Linear (Resistive) Region

Penn ESE370 Fall DeHon 16 Dimensions Channel Length (L) Channel Width (W) Oxide Thickness (T ox )

Preclass Ids for identical transistors in parallel? Penn ESE370 Fall DeHon 17

Preclass Ids for identical transistors in series? –(Vds small) Penn ESE370 Fall DeHon 18

Transistor Strength (W/L) Penn ESE370 Fall DeHon 19 S D

Transistor Strength (W/L) Shape dependence match Resistance intuition –Wider = parallel resistors  decrease R –Longer = series resistors  increase R Penn ESE370 Fall DeHon 20 S D

L drawn vs. L effective Doping not perfectly straight Spreads under gate Effective L smaller than draw gate width Penn ESE370 Fall DeHon 21

Channel Voltage Voltage varies along channel Think of channel as resistor Penn ESE370 Fall DeHon 22

Preclass 2 What is voltage in the middle of a resistive medium? –(halfway between terminals) Penn ESE370 Fall DeHon 23

Voltage in Channel Think of channel as resistive medium –Length = L –Area = Width * Depth(inversion) What is voltage in the middle of the channel? –L/2 from S and D ? Penn ESE370 Fall DeHon 24

Channel Voltage Voltage varies along channel If think of channel as resistor –Serves as a voltage divider between V S and V D Penn ESE370 Fall DeHon 25

Impact on Inversion What happens when –Vgs=2Vth ? –Vds=2Vth? What is Vmiddle-Vs? Penn ESE370 Fall DeHon 26

Channel Field When voltage gap V G -V x drops below V TH, drops out of inversion –Occurs when: V GS -V DS < V TH –What does this mean about conduction? Penn ESE370 Fall DeHon 27

Preclass 3 What is Vm? Penn ESE370 Fall DeHon 28

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 –What is voltage at Vmiddle if conduction stops? –What does that mean about conduction? Penn ESE370 Fall DeHon 29

Contradiction? Vg-Vx < Vt  cutoff (no current) No current  Vg-Vx=Vgs Vg-Vx=Vgs > Vt  current flows Penn ESE370 Fall DeHon 30

Way out? Vg-Vx < Vt  cutoff (no current) No current  Vg-Vx=Vgs Vg-Vx=Vgs > Vt  current flows Penn ESE370 Fall DeHon 31 Act like Vds at Vgs-Vt

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” Penn ESE370 Fall DeHon 32

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 33

Pinch Off When voltage drops below V T, drops out of inversion –Occurs when: V GS -V DS < V T Conclusion: –current cannot increase with V DS once V DS > V GS -V T Penn ESE370 Fall DeHon 34

Saturation In saturation, V DS-effective =V x = V GS -V T Becomes: Penn ESE370 Fall DeHon 35

Saturation V DS > V GS -V T Penn ESE370 Fall DeHon 36

Penn ESE370 Fall DeHon 37 Blue curve marks transition from Linear to Saturation Saturation Region

Class Ended Here Penn ESE370 Fall DeHon 38

Switching Operation Consider Inverter Start with in=0V Output voltage? What does first-order model say about NFET? Penn ESE370 Fall DeHon 39

Switching Operation Input rises from 0V When cross into new region? What region cross into? Ids Current? What happens to Ids as V continues to rise? What is happening to Vout? Penn ESE370 Fall DeHon 40

Switching Operation Input at Vdd When NFET change operating regions? Which region move into? What’s happening to Vout? What region when settles to static voltage? Penn ESE370 Fall DeHon 41

Penn ESE370 Fall DeHon 42 Retrace Transition

Approach Identify Region Drives governing equations Use to understand operation Penn ESE370 Fall DeHon 43

Big Idea 3 Regions of operation for MOSFET –Subthreshold –Resistive –Saturation Penn ESE370 Fall DeHon 44

Admin Text – highly recommend read –Second half on Friday HW4 out –Get started over weekend Penn ESE370 Fall DeHon 45