Lecture Outline. ESE 570: Digital Integrated Circuits and VLSI Fundamentals. Review: MOS Capacitor with External Bias

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1 ESE 57: Digital Integrated Circuits and VLSI Fundamentals Lec 5: Januar 6, 17 MOS Operating Regions, pt. 1 Lecture Outline! 3 Regions of operation for MOSFET " Subthreshold " Linear " Saturation! Level 1 Model Review: MOS Capacitor with External Bias! Three Regions of Operation: " Accumulation Region V G < " Depletion Region V G >, small " Inversion Region V G, large Review: MOS Capacitor with External Bias! Three Regions of Operation: " Accumulation Region V G < " Depletion Region V G >, small " Inversion Region V G, large Subthreshold/cutoff Above threshold Subthreshold/cutoff Above threshold Penn ESE 57 Spring 17 Khanna 3 Penn ESE 57 Spring 17 Khanna 4 Review: MOS Capacitor with External Bias Review: nmos = MOS cap + source/drain! Three Regions of Operation: " Subthreshold/Cutoff Region V G < V SB = V G V D V S " Above threshold/inversion Region V G x d = ε Si Φ Fp V SB q N A Subthreshold/cutoff Above threshold Penn ESE 57 Spring 17 Khanna 5 Penn ESE 57 Spring 17 Khanna 6 1

2 Review: Threshold Voltage MOSFET IV Characteristics 5 V for V SB = = = Φ GC Q ox C ox Φ F Q B C ox for V SB!= = +γ Φ F V SB Φ F γ = qn Aε Si C ox S Drain current [arbitrar unit] Penn ESE 57 Spring 17 Khanna Penn ESE 57 Spring 17 Khanna Gate to source voltage [V] Define: V th = Threshold Voltage 8 MOSFET IV Characteristics Cutoff Region << NMOS TRANSISTOR IN CUTOFF REGION V < H V G V D V S S V H V th Substrate or Bulk B p Depletion region Immobile acceptor ions No depletion or inversion laer under oxide, no current flow Penn ESE 57 Spring 17 Khanna V 9 1 Onset of Inversion Region = n + δ V = Linear Region V small, V < V G V D Q I Q B n + n + Channel acts like voltage controlled resistor Current flows proportional to V V As V D increases, channel depth at the drain decreases Depletion region, and thin inversion laer aka channel Thermal equilibrium in channel, no current flow 11 1

3 Channel Voltage! Voltage varies along channel! Channel acts as a resistor " Serves as a voltage divider between V S and V D = =L 13 V 14 = =L = =L Vd V Vs 15 Vd V Vs 16 Linear/Saturation Region Edge V = = =L Vd V Vs 17 n + n + Voltage divider along channel, until pinch off As V D increases, channel depth at the drain decreases 18 3

4 Channel Field! hen voltage gap V G V drops below V th, channel drops out of inversion Saturation Region V > " If V = V th # V =V G V D = V th V V AT Vx = V AT n + z n + 19 Channel Field Linear Region! hen voltage gap V G V drops below V th, drops out of inversion " hat if V > V th #V > V th? " Upper limit on current, channel is pinched off " nmos current saturated V small, V < n + z n + 1 Linear Region Linear Region V small, V < n + z n + V Boundar Conditions: V= = V S =, V=L = V =V D Mobile charge in inverted channel: Q I = C ox [ V ] z x d dr = µ n µ n = electron mobilit = cm /V sec 3 4 4

5 Linear Region d Q I = C ox [ V ] dr = µ n dv dv CS I C = dr = D µ n d µ n dv C = d Linear Region # L V V V V & GS T Integrate along the channel: V= = V S =, V=L = V k k = k L L V d = µ n dv C L = µ n V V C dv C L V V V V GS T 5 = k L V V = k V V = V AT = V = V AT and V AT = Assumptions: LINEAR SAT V = V AT = sat L V T SAT IN GENERAL sat 7 8 Saturation Saturation SAT V AT ΔL n + n+ V > L L V GS & L empiricall ΔL V V AT L 1 λ V If λv <<1, L 1 λ V 1+ λ V SAT L L V GS & L empricall ΔL V V AT L 1 λ V If λv <<1, L 1 λ V 1+ λ V L 1+ λ V 9 3 5

6 # L V V & # L V V & L V T 1+ λ V L V T 1+ λ V V = V AT λ= λ= 31 3 # L V V V V & GS T 1+ λ V # L V V V V & GS T 1+ λ V L V T 1+ λ V V = V AT λ= Level 1 model λv <<1 L V T 1+ λ V V = V AT λ= 33 34, V SB nmos IV Characteristics = +γ Φ F V SB Φ F # L V V V V V & GS T SB 1+ λ V L V SB 1+ λ V = f,v,v SB V Tn Cutoff/Subthreshold µ = n & L V V V GS Tn SB V V 1+ λ V > n,v < n Linear/Resistive µ n L V V V GS Tn SB 1+ λ V > n,v n Saturation

7 pmos IV Characteristics Measurement of Parameters k, γ D V Tp µ = p L Cutoff/Subthreshold & V V V GS Tp SB V V 1+ λ V < p,v > p Linear/Resistive µ p L V V V GS Tp SB 1+ λ V < p,v p Saturation G S B => SA T Measurement of Parameters λ Big Idea => SAT! 3 Regions of operation for MOSFET " Subthreshold " Linear " Saturation " Pinch Off " Channel length modulation! Level 1 Model " =f, V, V SB " Empirical measured parameters: k, γ,λ 39 4 Admin! H 3 due Thursda, / " Posted tonight after class " Gets ou started with Cadence " Make sure ou can access Cadence tonight or tomorrow " Don t wait until night before homework is due Penn ESE 57 Spring 17 Khanna 41 7