1. Spring 2007EE130 Lecture 40, Slide 1 Lecture #40 OUTLINE The MOSFET: Velocity saturation Reading: Chapter 19.1

2. Spring 2007EE130 Lecture 40, Slide 2 Velocity saturation limits I DSsat in modern MOSFETS Simple model:  sat is the electric field at velocity saturation: Velocity Saturation for    sat for  <   sat

3. Spring 2007EE130 Lecture 40, Slide 3 MOSFET I-V with Velocity Saturation In the linear region:

4. Spring 2007EE130 Lecture 40, Slide 4 Drain Saturation Voltage V DSsat 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

5. Spring 2007EE130 Lecture 40, Slide 5 Question: For V GS = 1.8 V, find the V DSsat of an NFET with T oxe = 3 nm, V T = 0.25 V, and W T = 45 nm, if L = (a) 10  m, (b) 1 um, (c) 0.1  m, and (d) 0.05  m Solution: From V GS, V T, and T oxe,  n is 200 cm 2 V -1 s -1.  sat = 2v sat /  n  = 8  10 4 V/cm m = 1 + 3T oxe /W T = 1.2 EXAMPLE: Drain Saturation Voltage

6. Spring 2007EE130 Lecture 40, Slide 6 (a) L = 10  m: V DSsat = (1/1.3V + 1/80V) -1 = 1.3 V (b) L = 1  m: V DSsat = (1/1.3V + 1/8V) -1 = 1.1 V (c) L = 0.1  m: V DSsat = (1/1.3V + 1/.8V) -1 = 0.5 V (d) L = 0.05  m: V DSsat = (1/1.3V + 1/.4V) -1 = 0.3 V

7. Spring 2007EE130 Lecture 40, Slide 7 Substituting V DSsat for V DS in the linear-region I DS eq’n. gives: For very short channel length: I DSsat is proportional to V GS –V T rather than (V GS – V T ) 2 I DSsat is not dependent on L I DSsat with Velocity Saturation

8. Spring 2007EE130 Lecture 40, Slide 8 Short-channel MOSFET: 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 Short- vs. Long-Channel MOSFET

9. Spring 2007EE130 Lecture 40, Slide 9 Velocity Overshoot When L is comparable to or less than the mean free path, some of the electrons travel through the channel without experiencing a single scattering event  projectile-like motion (“ballistic transport”)  The average velocity of carriers exceeds v sat e.g. 35% for L = 0.12  m NMOSFET  Effectively, v sat and  sat increase when L is very small

10. Spring 2007EE130 Lecture 40, Slide 10 Summary: NMOSFET I-V Linear region: Saturation region:

11. Spring 2007EE130 Lecture 40, Slide 11 PMOSFET I-V with Velocity Saturation Linear region: Saturation region: