Lecture 13: Part I: MOS Small-Signal Models

1. Lecture 13:Part I: MOS Small-Signal Models Prof. Niknejad

2. Lecture Outline • MOS Small-Signal Model (4.6) • Diode Currents in forward and reverse bias (6.1-6.3) University of California, Berkeley

3. Total Small Signal Current Transconductance Conductance University of California, Berkeley

4. Role of the Substrate Potential Need not be the source potential, but VB< VS Effect: changes threshold voltage, which changes the drain current … substrate acts like a “backgate” Q = (VGS, VDS, VBS) University of California, Berkeley

5. Backgate Transconductance Result: University of California, Berkeley

6. Four-Terminal Small-Signal Model University of California, Berkeley

7. MOSFET Capacitances in Saturation Gate-source capacitance: channel charge is not controlled by drain in saturation. University of California, Berkeley

8. Gate-Source Capacitance Cgs Wedge-shaped charge in saturation  effective area is (2/3)WL (see H&S 4.5.4 for details) Overlap capacitance along source edge of gate  (Underestimate due to fringing fields) University of California, Berkeley

9. Gate-Drain Capacitance Cgd Not due to change in inversion charge in channel Overlap capacitance Cov between drain and source is Cgd University of California, Berkeley

10. Junction Capacitances Drain and source diffusions have (different) junctioncapacitances since VSB and VDB = VSB + VDS aren’t the same Complete model (without interconnects) University of California, Berkeley

11. P-Channel MOSFET Measurement of –IDp versus VSD, with VSG as a parameter: University of California, Berkeley

12. Square-Law PMOS Characteristics University of California, Berkeley

13. Small-Signal PMOS Model University of California, Berkeley

14. MOSFET SPICE Model Many “levels” … we will use the square-law “Level 1” model See H&S 4.6 + Spice refs. on reserve for details. University of California, Berkeley

15. Part II: Currents in PN Junctions

16. Minority Carrier Close to Junction Thermal Generation - - - - - - - - - - - - - p-type n-type − − − + Carrier with energy below barrier height + Recombination + + + + + + + + + + + + + − Diode under Thermal Equilibrium • Diffusion small since few carriers have enough energy to penetrate barrier • Drift current is small since minority carriers are few and far between: Only minority carriers generated within a diffusion length can contribute current • Important Point: Minority drift current independent of barrier! • Diffusion current strong (exponential) function of barrier University of California, Berkeley

17. - - - - - - - + p-type n-type + + + + + + − + Reverse Bias • Reverse Bias causes an increases barrier to diffusion • Diffusion current is reduced exponentially • Drift current does not change • Net result: Small reverse current University of California, Berkeley

18. - - - - - - - + p-type n-type + + + + + + − + Forward Bias • Forward bias causes an exponential increase in the number of carriers with sufficient energy to penetrate barrier • Diffusion current increases exponentially • Drift current does not change • Net result: Large forward current University of California, Berkeley

19. Diode I-V Curve • Diode IV relation is an exponential function • This exponential is due to the Boltzmann distribution of carriers versus energy • For reverse bias the current saturations to the drift current due to minority carriers University of California, Berkeley

20. (minority) hole conc. on n-side of barrier (majority) hole conc. on p-side of barrier (Boltzmann’s Law) Minority Carriers at Junction Edges Minority carrier concentration at boundaries of depletion region increase as barrier lowers … the function is University of California, Berkeley

21. “Law of the Junction” Minority carrier concentrations at the edges of the depletion region are given by: Note 1: NA and ND are the majority carrier concentrations on the other side of the junction Note 2: we can reduce these equations further by substituting VD = 0 V (thermal equilibrium) Note 3: assumption that pn << ND and np << NA University of California, Berkeley

22. Minority Carrier Concentration Minority Carrier Diffusion Length The minority carrier concentration in the bulk region for forward bias is a decaying exponential due to recombination University of California, Berkeley

23. Steady-State Concentrations Assume that none of the diffusing holes and electrons recombine  get straight lines … This also happens if the minority carrier diffusion lengths are much larger than Wn,p University of California, Berkeley

24. Diode Current Densities University of California, Berkeley

25. n-well Fabrication of IC Diodes • Start with p-type substrate • Create n-well to house diode • p and n+ diffusion regions are the cathode and annode • N-well must be reverse biased from substrate • Parasitic resistance due to well resistance cathode annode p p+ n+ p-type p-type University of California, Berkeley

26. Diode Small Signal Model • The I-V relation of a diode can be linearized University of California, Berkeley

27. Diode Capacitance • We have already seen that a reverse biased diode acts like a capacitor since the depletion region grows and shrinks in response to the applied field. the capacitance in forward bias is given by • But another charge storage mechanism comes into play in forward bias • Minority carriers injected into p and n regions “stay” in each region for a while • On average additional charge is stored in diode University of California, Berkeley

28. Charge Storage • Increasing forward bias increases minority charge density • By charge neutrality, the source voltage must supply equal and opposite charge • A detailed analysis yields: Time to cross junction (or minority carrier lifetime) University of California, Berkeley

29. Diode Circuits • Rectifier (AC to DC conversion) • Average value circuit • Peak detector (AM demodulator) • DC restorer • Voltage doubler / quadrupler /… University of California, Berkeley