ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems. Today. Refinement. Last Time. No Field. Body Contact
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1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 10: September 6, 01 MOS Transistor Basics Today MOS Transistor Topology Threshold Operating Regions Resistive Saturation Velocity Saturation Subthreshold 1 Last Time Refinement 3 Depletion region excess carriers depleted 4 Body Contact No Field Fourth terminal Also effects fields Usually common across transistors V GS =0, V =
2 Apply V GS >0 Channel Evolution Increasing Vgs Accumulate negative charge Repel holes (fill holes) Gate Capacitance Changes based on operating region. Happy if you treat as parallel plate Capacitor for HW4. Inversion Surface builds electrons Inverts to n-type Draws electrons from n + source 9 10 Threshold Voltage where strong inversion occurs threshold voltage φ Around ϕ F = φ T ln N A F n i Engineer by controlling doping (N A ) Resistive Region V GS >V T, V small C OX = ε OX t OX W C OX ( V V T )V 11 1
3 Resistive Region Linear (Resistive) Region V GS >V T, V small V GS fixed looks like resistor Current linear in V C OX = ε OX t OX W C OX ( V V T )V Linear (Resistive) Region Blue curve marks transition from Linear to Saturation Channel Length (L) Channel Width (W) Oxide Thickness (T ox ) Dimensions Preclass Preclass Ids for identical transistors in parallel? Ids for identical transistors in series? (Vds small)
4 Transistor Strength (W/L) S D Transistor Strength (W/L) S D C OX = ε OX t OX Shape dependence match Resistance intuition Wider = parallel resistors decrease R Longer = series resistors increase R R = ρl A W C OX ( V V T )V W C OX ( V V T )V 19 0 L drawn vs. L effective Channel Voltage Doping not perfectly straight Spreads under gate Effective L smaller than draw gate width Voltage varies along channel Think of channel as resistor 1 Preclass Voltage in Channel What is voltage in the middle of a resistive medium? (halfway between terminals) Think of channel as resistive medium Length = L Area = Width * Depth(inversion) What is voltage in the middle of the channel? L/ from S and D? 3 4 4
5 Channel Voltage Impact on Inversion Voltage varies along channel If think of channel as resistor Serves as a voltage divider between V S and V D What happens when Vgs=Vth? Vds=Vth? What is Vmiddle-Vs? 5 6 Channel Field Preclass 3 When voltage gap V G -V x drops below V TH, drops out of inversion What is Vm? Occurs when: V GS -V < V TH What does this mean about conduction? 7 8 Channel Field When voltage gap V G -V x drops below V T, drops out of inversion Occurs when: V GS -V < V T What is voltage at Vmiddle if conduction stops? What does that mean about conduction? Contradiction? Vg-Vx < Vt cutoff (no current) No current Vg-Vx=Vgs Vg-Vx=Vgs > Vt current flows
6 Way out? Channel Field Vg-Vx < Vt cutoff (no current) No current Vg-Vx=Vgs Vg-Vx=Vgs > Vt current flows Act like Vds at Vgs-Vt When voltage gap V G -V x drops below V T, drops out of inversion Occurs when: V GS -V < V T Channel is pinched off 31 3 Channel Field When voltage gap V G -V x drops below V T, drops out of inversion Occurs when: V GS -V < V T Channel is pinched off Current will flow, but cannot increase any further Pinch Off When voltage drops below V T, drops out of inversion Occurs when: V GS -V < V T Conclusion: current cannot increase with V once V > V GS -V T Saturation Saturation In saturation, V -effecitve =V x = V GS -V T W C OX ( V V T )V Becomes: W C OX V V T ( ( ) V GS V T ) 35 V > V GS -V T W C OX V V T C OX ( ( ) V GS V T ) W L V GS V T [( ) ] 36 6
7 Saturation Region Blue curve marks transition from Linear to Saturation Preclass 3 What is electrical field in channel? L eff =5nm, V =1V Field = V /L Velocity: v=f*µ Electron mobility: µ n = 500 cm /V What is electron velocity? 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 How relate to preclass 3 velocity? Encounter when channel short Modern processes, L is short enough S D Velocity Saturation Once velocity saturates: ν sat C OX W V GS V T V AT V AT Lν sat µ n Velocity Saturation Below Threshold Transition from insulating to conducting is non-linear, but not abrupt Current does flow But exponentially dependent on V GS
8 W = I S e L Subthreshold V GS nkt / q 1 e V kt / q 1+ λv ( ) Subthreshold W/L dependence follow from resistor behavior (parallel, series) Not shown explicitly in text λ is a channel width modulation effect W = I S e L V GS nkt / q 1 e V kt / q S 1+ λv ( ) D Subthreshold Slope Exponent in V GS determines how steep the turnoff is Every S Volts S = n kt ln( 10) Divide by 10 q W = I S e L V GS nkt / q 1 e V kt / q 1+ λv ( ) 45 Subthreshold Slope Exponent in V GS determines how steep the turnoff is Every S Volts (S not related to source) Divide by 10 S = n kt ln 10 q n depends on electrostatics n=1 S=60mV at Room Temp. (ideal) n=1.5 S=90mV Single gate structure showing S=90-110mV ( ) 46 vs. V GS Admin Text 3.3. highly recommend read Second half on Friday HW3 due Thursday HW4 out
9 3 Regions of operation for MOSFET Subthreshold Resistive Saturation Pinch Off Velocity Saturation Short channel Big Idea 49 9
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