ESE370: ircuitlevel Modeling, Design, and Optimization for Digital Systems Lec 7: September 20, 2017 MOS Transistor Operating Regions Part 1 Today! PN Junction! MOS Transistor Topology! Threshold! Operating Regions " Resistive " Saturation " Subreshold (next class) " Velocity Saturation (next class) 1 2 Doped Silicon PN Junction Ptype Ntype =hole Excess holes Excess electrons Penn ESE 370 Fall 2017 Khanna 4 PN Junction PN Junction Penn ESE 370 Fall 2017 Khanna Hole Diffusion Ptype Electron Diffusion Ntype PN junction causes a depletion region to form Electrons diffuse from Ntype to Ptype Holes diffuse from Ptype to Ntype Diffusion current caused by diffusion of carriers =hole 5 Hole Diffusion Electron Drift Ptype Hole Drift Electron Diffusion PN junction causes a depletion region to form Electrons diffuse from Ntype to Ptype Holes diffuse from Ptype to Ntype Diffusion current caused by diffusion of carriers Equilibrium achieved when V bi, builtin potential, is formed across e depletion region Drift current cause by Efield due to V bi to counteract diffusion current Penn ESE 370 Fall 2017 Khanna 6 Ntype =hole 1
Drift/Diffusion urrents PN Junction Forward Biasing! Diffusion current " urrent caused by semiconductor diffusion of holes and electrons! Drift current " urrent due to movement of holes and electrons caused by force from potential difference induced efield Ptype Applied Efield Depletion Efield Ntype =hole + Penn ESE 370 Fall 2017 Khanna 7 Forward biasing connect positive terminal to ptype and negative terminal to ntype Holes/electrons pushed towards depletion region, causing it to narrow The applied voltage efield continues to narrow e depletion region (i.e reduce e depletion efield) current flows rough e device from ptype to ntype Penn ESE 370 Fall 2017 Khanna 8 PN Junction Reverse Biasing Last Time MOS model Ptype Depletion Efield + Ntype =hole Reverse biasing connect positive terminal to ntype and negative terminal to ptype Holes/electrons attracted away from depletion region, causing it to widen No current flows rough e device If reverse bias increases past breakdown voltage, e depletion efield increases until breakdown occurs and reverse biased current flows causing ermal damage to junction Penn ESE 370 Fall 2017 Khanna 9 + + + + + NMOS gate drain source semiconductor V gs >0 onducts + + + + + PMOS V gs >0 onduction 10 Refinement Bulk/Body ontact! Depletion region excess carriers depleted! MOS actually has four contacts! Also effects fields! Usually common across transistors " Gnd for nmos, V dd for pmos D G B S 11 12 2
No Field! V GS =0, V =0 Apply V GS >0! Accumulate negative charge " Repel holes + + + + + + + 13 14 hannel Evolution Increasing Vgs Gate apacitance hanges based on operating region. 15 16 Gate apacitance hannel Evolution Increasing Vgs ox dep! Depletion capacitance dependent on wid of depletion region and potential at siliconoxide interface 17 18 3
Inversion Threshold! Surface builds electrons " Inverts to ntype " Draws electrons from n + source terminal! Voltage where strong inversion occurs reshold voltage " V ~= 2ϕ F " Engineer by controlling doping (N A ) φ F = kt q ln N A n i 19 20 Linear Region Linear Region! V GS >V and V small OX = ε OX t OX 2 21 22 Linear Region MOSFET IV haracteristics! V GS >V and V small! V GS fixed looks like resistor V <V GS V TH " urrent linear in V 2 µ n W OX ( L )( V V GS )V V V GS V TH V GS V V 23 V 24 4
Preclass Preclass! I ds for identical transistors in parallel?! I ds for identical transistors in series? " (Vds small) 25 26 Dimensions Transistor Streng (W/L)! hannel Leng (L)! hannel Wid (W)! Oxide Thickness (T ox ) OX = ε OX t OX 2 2 27 28 Transistor Streng (W/L) L drawn vs. L effective! Shape dependence match Resistance intuition " Wider = parallel resistors decrease R " Longer = series resistors increase R! Doping not perfectly straight! Spreads under gate! Effective L smaller an draw gate wid R = ρl A 2 29 30 5
hannel Voltage Preclass! Voltage varies along channel! Think of channel as resistor! What is voltage in e middle of a resistive medium? " (halfway between terminals) 31 32 Voltage in hannel hannel Voltage! Think of channel as resistive medium " Leng = L " Area = W * Dep(inversion)! What is voltage in e middle of e channel? " L/2 from S and D?! Voltage varies along channel! If ink of channel as resistor " Serves as a voltage divider between V S and V D 33 34 Voltage along hannel Voltage along hannel! What does voltage along e channel look like?! What does voltage along e channel look like? x=0 x=l x=0 x=l V(x) x 35 Vd V(x) Vs x 36 6
Voltage along hannel! What does voltage along e channel look like? Voltage along hannel! What does voltage along e channel look like? x=0 x=l x=0 x=l Vd V(x) Vs x 37 Vd V(x) Vs x 38 hannel Field hannel Field! When voltage gap V G V x drops below V, drops out of inversion! When voltage gap V G V x drops below V, drops out of inversion " Saturation Edge: V = V GS V V G V X (@ D) = V V x V x 39 40 hannel Field hannel Field! When voltage gap V G V x drops below V, drops out of inversion " Deep Saturation: V > V GS V V G V X (@ D) =?! When voltage gap V G V x drops below V, drops out of inversion " Deep Saturation: V > V GS V V G V X (@ D) < V Upper limit on current, channel is pinched off V x V x 41 42 7
Pinch Off Saturation! When voltage along e channel drops below V, e channel drops out of inversion " Occurs when: V G V X (@ D) < V V > V GS V! onclusion: " current cannot increase wi V once V > V GS V T " Not true! More later! In saturation, V effective =V x = V GS V T " W ) OX ( V L GS V T )V V 2, +. * 2! Becomes: " W ) OX + V L GS V T * + = µ " n OX W V 2 L GS V T ( ( ) 2 V V GS T ) 2 2 [( ) 2 ],.. 43 44 MOSFET IV haracteristics Approach V <V GS V TH V GS V! Identify Region! Drives governing equations " See preclass reference! Use region and equations to understand operation V V GS V TH V 45 46 Big Idea Admin! 3 Regions of operation for MOSFET " Subreshold " Linear " Saturation! Text 3.3.2 highly recommend read!! " Second half on Friday! HW4 out " Get started over weekend " Long and timeconsuming 47 48 8