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EE130/230A Discussion 12 Peng Zheng 1

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Velocity Saturation Velocity saturation limits I Dsat in sub-micron MOSFETS Simple model: E sat is the electric field at velocity saturation: for sat for < sat Lecture 22, Slide 2EE130/230A Fall 2013

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Drain Saturation Voltage, V Dsat If sat L >> V GS -V T then the MOSFET is considered “long-channel”. This condition can be satisfied when – L is large, or – V GS is close to V T Lecture 22, Slide 3EE130/230A Fall 2013 Current saturation is limited by 2 mechanisms: 1.Pinch-off 2.Velocity saturation

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Example: Drain Saturation Voltage Question: For V GS = 1.8 V, find V Dsat for an NMOSFET with T oxe = 3 nm, V T = 0.25 V, and W T = 45 nm, if L = (a) 10 m, (b) 1 m, (c) 0.1 m (d) 0.05 m Solution: From V GS, V T and T oxe, eff is 200 cm 2 V -1 s -1. E sat = 2v sat / eff = 8 10 4 V/cm m = 1 + 3T oxe /W T = 1.2 Lecture 22, Slide 4EE130/230A Fall 2013

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(a) L = 10 m: V Dsat = (1/1.3V + 1/80V) -1 = 1.3 V (b) L = 1 m: V Dsat = (1/1.3V + 1/8V) -1 = 1.1 V (c) L = 0.1 m: V Dsat = (1/1.3V + 1/.8V) -1 = 0.5 V (d) L = 0.05 m: V Dsat = (1/1.3V + 1/.4V) -1 = 0.3 V Lecture 22, Slide 5EE130/230A Fall 2013

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MOSFET I-V with Velocity Saturation In the linear region: Lecture 22, Slide 6EE130/230A Fall 2013

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I Dsat with Velocity Saturation Substituting V Dsat for V DS in the linear-region I D equation gives For very short L: I Dsat is proportional to V GS –V T rather than (V GS – V T ) 2 I Dsat is not dependent on L Lecture 22, Slide 7EE130/230A Fall 2013

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Short- vs. Long-Channel NMOSFET Short-channel NMOSFET: I Dsat is proportional to V GS -V Tn rather than (V GS -V Tn ) 2 V Dsat is lower than for long-channel MOSFET Channel-length modulation is apparent Lecture 22, Slide 8EE130/230A Fall 2013 C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 6-23

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The Short Channel Effect (SCE) |V T | decreases with L – Effect is exacerbated by high values of |V DS | This effect is undesirable (i.e. we want to minimize it!) because circuit designers would like V T to be invariant with transistor dimensions and bias condition “V T roll-off” Lecture 22, Slide 9EE130/230A Fall 2013 R. F. Pierret, Semiconductor Device Fundamentals, Fig. 19.3

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depletion charge supported by gate (simplified analysis) n+n+ n+n+ VGVG p depletion region Large L: SD Small L: DS Depletion charge supported by S/D The smaller L is, the greater the percentage of depletion charge balanced by the S/D pn junctions: rjrj Lecture 22, Slide 10EE130/230A Fall 2013

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V T Roll-Off: First-Order Model Minimize V T by reducing T oxe reducing r j increasing N A (trade-offs: degraded eff, m) MOSFET vertical dimensions should be scaled along with horizontal dimensions! Lecture 22, Slide 11EE130/230A Fall 2013 R. F. Pierret, Semiconductor Device Fundamentals, Fig. 19.4

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Questions? 1. CMOS fabrication process / technology? 2. The MOSFET design project? 12 Good luck to Quiz#5!

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