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 =0 5 6 1
Apply V GS >0 Channel Evolution Increasing Vgs Accumulate negative charge Repel holes (fill holes) + + + + + + + + - - - - - - - - - 7 8 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
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 13 14 Linear (Resistive) Region Blue curve marks transition from Linear to Saturation Channel Length (L) Channel Width (W) Oxide Thickness (T ox ) Dimensions 15 16 Preclass Preclass Ids for identical transistors in parallel? Ids for identical transistors in series? (Vds small) 17 18 3
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
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 9 30 5
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 33 34 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
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? 37 38 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 39 40 Velocity Saturation Below Threshold Transition from insulating to conducting is non-linear, but not abrupt Current does flow But exponentially dependent on V GS 41 4 7
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 43 44 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 47 48 8
3 Regions of operation for MOSFET Subthreshold Resistive Saturation Pinch Off Velocity Saturation Short channel Big Idea 49 9