MOS Transistor. EE141-Fall 2007 Digital Integrated Circuits. Review: What is a Transistor? Announcements. Class Material

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1 EE-Fall 7 igital Integrated Circuits MO Transistor Lecture MO Transistor Model Announcements Review: hat is a Transistor? Lab this week! Lab next week Homework # is due Thurs. Homework # due next Thurs. A MO Transistor V A witch! V V T R on Class Material witch Model of MO Transistor Last lecture CMO manufacturing process esign rules Today s lecture MO transistor modeling ill see how to use these models to understand tradeoffs between CMO gate delay, power, etc. Reading (..-.. V V < V T V > V T R on 6 6

2 Threshold Voltage: Concept V + Transistor with ate and rain Bias V V I n-channel p-substrate epletion region V(x + L x B ith positive gate bias, electrons pulled toward the gate ith large enough bias, enough electrons will be pulled to "invert" the surface (p n type Voltage at which surface inverts: magic threshold voltage V T p-substrate B 7 7 The Threshold Voltage Threshold ( φ + V φ VT = VT + γ F B Fermi potential N φ A F = φt ln ni Φ F is approximately.6v for p-type substrates γ is the body factor V T is approximately.v for our process F The rain Current Charge density in the channel is controlled by the gate voltage: εox Qi ( x = Cox [ V V( x VT ] Cox = tox rain current is proportional to charge times velocity: I = υn( x Qi ( x dv υ n( x = µ n ξ( x = µ n dx 8 8 The Body Effect V T (V reverse body bias V (V B V T 9 9 The rain Current Combining velocity and charge: I = [ υn( x Qi( x ] I = µ n Cox VT dv dx Integrating over the channel: V I = ( k n V VT V L µ n ε k ox n = µ n Cox = t ox

3 Plot of I-V I V Curve aturation For (V V T < V, the effective drain voltage and current saturate: ( V = V V, eff T kn I = L T Is this really what happens? Of course, real drain current isn t totally independent of V For example, approx. for channel-length modulation: k n I = ( V VT ( + λ V L 6 6 Cause of the Problem hy does the current bend down? Modes of Operation Cutoff: V -V T < I = hen (V -V TH -V is negative, in our analysis the sign of the carriers changes But transistors don t actually behave this way Look at what really happens to channel charge: Linear (Resistive: V -V T > V aturation: < V -V T < V I = kn L kn I = L V T V T 7 7 Transistor in aturation < V - V T < V n+ - V V - V T + V > V - V T n+ Current-Voltage Relations: A ood Ol Transistor I (A x 6 V =. V Resistive aturation V =. V V = V -V T V =. V Quadratic Relationship Pinch-off V =. V... V (V 8 8

4 A Model for Manual Analysis I I = k with V > V V T aturation: k n I = T L V < V V T n ( + λ V L Linear: V T V ( φ + V φ VT = VT + γ F B F Velocity aturation I V = V V AT V -V T Long-channel device hort-channel device V 9 9 Current-Voltage Relations: The eep ub-micron Transistor I (A... x Early V =. V aturation V =. V V =. V V =. V... V (V Linear Relationship I (A I versus V 6 x quadratic... V (V Long Channel (L=.µm quadratic... V (V I (A. x.. linear hort Channel (L=.µm Velocity aturation Velocity saturates due to carrier scattering effects υ n (m/s υ sat = Constant velocity Including Velocity aturation Approximate velocity: Continuity requires that: ξ = υ µ c sat n Integrating to find the current again: Constant mobility (slope = µ ξ c ξ (V/µm

5 Velocity aturation rain Current aturation occurs when carriers reach I = Cox T VAT υsat υ sat e also know that: µ ncox V AT I = T VAT + ( VAT ξcl L implified Velocity aturation (cont (cont d Assume V AT = ξ c L when (V V T > ξ c L V AT (V ξ c L Actual V AT Equating the two expressions gives V AT and I : ( ξ ( ξ ( ( ξ V VT cl V VT VAT = I = υsatcox V V + L V V + L T c T c ξ c L V -V T (V 8 8 I (A Regions of Operation 6 x V =. V Resistive aturation V =. V V = V -V T V =. V V =. V... V (V Long Channel (L=.µm V AT. x V =. V I (A.. /L=. Resistive Velocity aturation V (V V -V T hort Channel (L=.µm V =. V V =. V V =. V implified Model efine V T = V V T, V VAT = ξ c L I (A. x.. Linear V = V VAT V = V T Velocity aturation... V (V V T = V VAT aturation 9 9 implified Velocity aturation Assume velocity linear until hit υ sat A Unified Model for Manual Analysis υ n (m/s υ sat = Constant velocity ξ c = υ sat /µ ξ (V/µm 7 7 I B define V T = V V T for V T : I = for V T : V I k V V V L, eff = ' T, eff + with V,eff = min (V T, V, V VAT ( λ

6 imple Model versus PICE. x V =V VAT Next Lecture Using the MO model: Inverter VTC and delay. I (A. V =V T... V (V Transistor Model for Manual Analysis V Textbook: page A PMO Transistor x V = -.V -. V = -.V -. All variables negative I prefer to work with absolute values I (A -.6 V = -.V -.8 V = -.V V (V

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